UBC Wiki - User contributions [en]

User:AndreaMameri

2012-03-27T17:52:07Z

AndreaMameri: /* BIOGRAPHY */

===BIOGRAPHY===

'''HELLOOOOOOO'''

===Pythagorean theorem===

To refresh the memory and for me to complete the assignment, I will talk to you a little about the Pythagorean Theorem. I will try to make this fun. (Math is never fun, sry)

The Pythagorean Theorem can only be completed when working with right angle triangle. This means that one of the angles which make up a triangle is 90 degrees. The triangle is then composed of different lines. The longest line in the triangle is called the HYPOTENUSE; it is usually located right across the 90 degree angle. In the Pythagorean Theorem the HYPOTENUSE is represented by the letter C.

The Pythagorean Theorem is: <math>a^2+b^2=c^2</math>

The remaining two sides are represented by the letter A and the letter B. The order does not matter.

If a problem is given, the variables need to be plugged into the formula. If the HYPOTENUSE is given, this is plugged into the C, if one of the sides is given then this is plugged into A or B. Whichever side you are solving for, you make the equation equal that.

Example:
One side of a right angle triangle is 5 cm. The other side is 12 cm. Solve for the HYPOTENUSE.

<math>a^2 + b^2 = c^2</math>

<math>5^2 + 12^2 = c^2</math>

<math>25 + 144 = c^2</math>

<math>169 = c^2</math>

<math>c^2 = 169</math>

<math>c = √169</math>

<math>c = 13</math>

===Calculus in economy===

As I mentioned earlier on, the faculty that I am currently in is Commerce in the Sauder School of Business. Surprisingly enough, for me anyway, math is a big part of Commerce. Here I will be discussing how calculus plays a very important part in finding the elasticity of the economic curve.

[[File:Elastic.jpg]]

First of all, I would like to explain what elasticity actually is. In economics, elasticity is the ratio of the percent change in one variable to the percent change in another variable. Elasticity is used to measure how responsive one variable is to the other. It is said that if a variable has high elasticity then if that one variable is changed then this would impact the other greatly. On the other hand, if the variable is said to have a low elasticity then this means that if that same variable is changed then nothing or little with happen to the other variable. So, when is elasticity used? Mainly when looking at price elasticity of demand, price elasticity of supply, income elasticity of demand. Elasticity is essential in economics (according to professor Gateman). It is useful in understanding the marginal theory. For example, what happens to consumption if one more product increases its prices.

The formula for elasticity is:

Elasticity = (percentage change in Z) / (percentage change in Y)

From the get go, we see 2 variables that might have a relationship to each other. This already plays a big part in calculus.

Using some fairly basic calcululus, we can show that
(percentage change in Z) / (percentage change in Y) = (dZ / dY)*(Y/Z)

where dZ/dY is the partial derivative of Z with respect to Y. Thus we can calculate any elasticity through the formula:

'''Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)'''

"A good or service is considered to be highly elastic if a slight change in price leads to a sharp change in the quantity demanded or supplied. Usually these kinds of products are readily available in the market and a person may not necessarily need them in his or her daily life. On the other hand, an inelastic good or service is one in which changes in price witness only modest changes in the quantity demanded or supplied, if any at all. These goods tend to be things that are more of a necessity to the consumer in his or her daily life."

Now… lets look at an example:

Demand is Q = 110 - 4P. What is price (point) elasticity at $5?

We saw that we can calculate any elasticity by the formula:
Y = (dQ / dp)*(P/Q)

That is the case in our demand equation of Q = 110 - 4P. Thus we differentiate with respect to P and get:
dQ/dP = -4

So we substitute dQ/dP = -4 and Q = 110 - 4P into our price elasticity of demand equation

Price elasticity of demand: = (dQ / dP)*(P/Q)

Price elasticity of demand: = (-4)*(P/(110-4P)

Price elasticity of demand: = -4P/(110-4P)

We want price elasticity at P = 5, so we substitute this into our price elasticity of demand equation:

= -4P/(110-4P)
= -20/90
= -2/9

Our price elasticity of demand is -2/9.

Since it is less than 1 > '''Demand is Price Inelastic'''

Bibliography:
http://www.investopedia.com/university/economics/economics4.asp

http://en.wikipedia.org/wiki/Elasticity_(economics)

http://economics.about.com/cs/micfrohelp/a/calculus_d.htm

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 13

2011-02-08T09:30:37Z

AndreaMameri: /* = */

Assingment:

Explain in your own words what it means that these concepts work on a '''logarithmic scale'''. Create a wiki page with all your explanations.

===

'''Brightness of stars'''

Taken straight from WIKI, what is logarithmic scale: "A logarithmic scale is a scale of measurement that uses the
logarithm of a physical quantity instead of the quantity itself".

what does this mean in plain english and when is this scale used?

It is basically the presentation of data that covers a wide range of data that are presented and very relavant. As well, lorgatithmic scales also consentrates on the changes of one specific constant, more specifically looking at its ratios.

What does this look like? An example that we saw in class.....

[[File:Loglog h600.png]]

The example of the use of these scale is looking at the Brightness of stars.

[[File:Star.jpg]] PRETTY RIGHT?!

Now that we have identified the question and highlighted its different components 1) logartihmic scale and 2) the brightness of stars... what do these two have to do with eachother? (very important question to be asking)

Well.. one of the mian properties of stars is their brightness. Putting this in a little context, the brightness of stars are measured through the magnitude system. Around 150 B.C.E, Hipparchus, a greek astronomer invented this method. What is bassically composed of was the classification of stars and their nrightness through the naked eye. He would classify how bright the stars looked. For the brightest ones he would put in the first magnitude, and for the dimmest lights he would put them in the sixth magnification.

As years went by, this system was improved and new ideas arrose. One of the most inovated changes was the idea of logarithmic scales. "It was thought that the eye sensed differences in brightness on a logarithmic scale so a star's magnitude is not directly proportional to the actual amount of energy you receive".

THE MATH:

On the quantified magnitude scale, a magnitude interval of 1 corresponds to a factor of 100^1/5 or approximately 2.512 times the amount in actual intensity.

For example, first magnitude stars are about 2.512^2-1 = 2.512 times brighter than 2nd magnitude stars, 2.512×2.512 = 2.512^3-1 = 2.512^2 times brighter than 3rd magnitude stars, 2.512×2.512×2.512 = 2.512^4-1 = 2.512^3 times brighter than 4th magnitude stars, etc.

===
Bibliography:
http://www.astronomynotes.com/starprop/s4.htm

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 13

2011-02-08T09:18:37Z

AndreaMameri: /* = */

File:Star.jpg

2011-02-08T09:18:02Z

AndreaMameri:

File:Loglog h600.png

2011-02-08T09:15:43Z

AndreaMameri:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 13

2011-02-08T09:12:49Z

AndreaMameri: /* = */

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 13

2011-02-08T09:05:10Z

AndreaMameri:

Assingment:

Explain in your own words what it means that these concepts work on a '''logarithmic scale'''. Create a wiki page with all your explanations.

===

'''Brightness of stars'''

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 13

2011-02-08T09:03:48Z

AndreaMameri: Created page with " kj<M"

kj<M

User:AndreaMameri

2011-01-28T10:49:39Z

AndreaMameri: /* Calculus in economy */

===BIOGRAPHY===

'''HELLOOOOOOO''' everyone who is interested in my page!!!!!!

My name is Andrea Mameri, I'm from Ecuador. I was actually born I Ecuador and stayed there for 10 years of my life. Then I moved to Angola-Luanda where i spent 5 years living there. After this shocking change of my life, my father decided to go back to his roots in Brazil. I spent 2 years in the busy city of Sao Paulo after moving to Canada to continue my education.

Since my father is from Brazil, this means that i had dual citizenship. Therefore, I am part Ecuadorian and part Brazilian.
Which one do i call home? Where ever my family is.

I am currently in the Sauder School of Business

===Pythagorean theorem===

To refresh the memory and for me to complete the assignment, I will talk to you a little about the Pythagorean Theorem. I will try to make this fun. (Math is never fun, sry)

The Pythagorean Theorem can only be completed when working with right angle triangle. This means that one of the angles which make up a triangle is 90 degrees. The triangle is then composed of different lines. The longest line in the triangle is called the HYPOTENUSE; it is usually located right across the 90 degree angle. In the Pythagorean Theorem the HYPOTENUSE is represented by the letter C.

The Pythagorean Theorem is: <math>a^2+b^2=c^2</math>

The remaining two sides are represented by the letter A and the letter B. The order does not matter.

If a problem is given, the variables need to be plugged into the formula. If the HYPOTENUSE is given, this is plugged into the C, if one of the sides is given then this is plugged into A or B. Whichever side you are solving for, you make the equation equal that.

Example:
One side of a right angle triangle is 5 cm. The other side is 12 cm. Solve for the HYPOTENUSE.

<math>a^2 + b^2 = c^2</math>

<math>5^2 + 12^2 = c^2</math>

<math>25 + 144 = c^2</math>

<math>169 = c^2</math>

<math>c^2 = 169</math>

<math>c = √169</math>

<math>c = 13</math>

===Calculus in economy===

As I mentioned earlier on, the faculty that I am currently in is Commerce in the Sauder School of Business. Surprisingly enough, for me anyway, math is a big part of Commerce. Here I will be discussing how calculus plays a very important part in finding the elasticity of the economic curve.

[[File:Elastic.jpg]]

First of all, I would like to explain what elasticity actually is. In economics, elasticity is the ratio of the percent change in one variable to the percent change in another variable. Elasticity is used to measure how responsive one variable is to the other. It is said that if a variable has high elasticity then if that one variable is changed then this would impact the other greatly. On the other hand, if the variable is said to have a low elasticity then this means that if that same variable is changed then nothing or little with happen to the other variable. So, when is elasticity used? Mainly when looking at price elasticity of demand, price elasticity of supply, income elasticity of demand. Elasticity is essential in economics (according to professor Gateman). It is useful in understanding the marginal theory. For example, what happens to consumption if one more product increases its prices.

The formula for elasticity is:

Elasticity = (percentage change in Z) / (percentage change in Y)

From the get go, we see 2 variables that might have a relationship to each other. This already plays a big part in calculus.

Using some fairly basic calcululus, we can show that
(percentage change in Z) / (percentage change in Y) = (dZ / dY)*(Y/Z)

where dZ/dY is the partial derivative of Z with respect to Y. Thus we can calculate any elasticity through the formula:

'''Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)'''

"A good or service is considered to be highly elastic if a slight change in price leads to a sharp change in the quantity demanded or supplied. Usually these kinds of products are readily available in the market and a person may not necessarily need them in his or her daily life. On the other hand, an inelastic good or service is one in which changes in price witness only modest changes in the quantity demanded or supplied, if any at all. These goods tend to be things that are more of a necessity to the consumer in his or her daily life."

Now… lets look at an example:

Demand is Q = 110 - 4P. What is price (point) elasticity at $5?

We saw that we can calculate any elasticity by the formula:
Y = (dQ / dp)*(P/Q)

That is the case in our demand equation of Q = 110 - 4P. Thus we differentiate with respect to P and get:
dQ/dP = -4

So we substitute dQ/dP = -4 and Q = 110 - 4P into our price elasticity of demand equation

Price elasticity of demand: = (dQ / dP)*(P/Q)

Price elasticity of demand: = (-4)*(P/(110-4P)

Price elasticity of demand: = -4P/(110-4P)

We want price elasticity at P = 5, so we substitute this into our price elasticity of demand equation:

= -4P/(110-4P)
= -20/90
= -2/9

Our price elasticity of demand is -2/9.

Since it is less than 1 > '''Demand is Price Inelastic'''

Bibliography:
http://www.investopedia.com/university/economics/economics4.asp

http://en.wikipedia.org/wiki/Elasticity_(economics)

http://economics.about.com/cs/micfrohelp/a/calculus_d.htm

User:AndreaMameri

2011-01-28T10:46:43Z

AndreaMameri: /* Calculus in economy */

===BIOGRAPHY===

'''HELLOOOOOOO''' everyone who is interested in my page!!!!!!

My name is Andrea Mameri, I'm from Ecuador. I was actually born I Ecuador and stayed there for 10 years of my life. Then I moved to Angola-Luanda where i spent 5 years living there. After this shocking change of my life, my father decided to go back to his roots in Brazil. I spent 2 years in the busy city of Sao Paulo after moving to Canada to continue my education.

Since my father is from Brazil, this means that i had dual citizenship. Therefore, I am part Ecuadorian and part Brazilian.
Which one do i call home? Where ever my family is.

I am currently in the Sauder School of Business

===Pythagorean theorem===

To refresh the memory and for me to complete the assignment, I will talk to you a little about the Pythagorean Theorem. I will try to make this fun. (Math is never fun, sry)

The Pythagorean Theorem can only be completed when working with right angle triangle. This means that one of the angles which make up a triangle is 90 degrees. The triangle is then composed of different lines. The longest line in the triangle is called the HYPOTENUSE; it is usually located right across the 90 degree angle. In the Pythagorean Theorem the HYPOTENUSE is represented by the letter C.

The Pythagorean Theorem is: <math>a^2+b^2=c^2</math>

The remaining two sides are represented by the letter A and the letter B. The order does not matter.

If a problem is given, the variables need to be plugged into the formula. If the HYPOTENUSE is given, this is plugged into the C, if one of the sides is given then this is plugged into A or B. Whichever side you are solving for, you make the equation equal that.

Example:
One side of a right angle triangle is 5 cm. The other side is 12 cm. Solve for the HYPOTENUSE.

<math>a^2 + b^2 = c^2</math>

<math>5^2 + 12^2 = c^2</math>

<math>25 + 144 = c^2</math>

<math>169 = c^2</math>

<math>c^2 = 169</math>

<math>c = √169</math>

<math>c = 13</math>

===Calculus in economy===

As I mentioned earlier on, the faculty that I am currently in is Commerce in the Sauder School of Business. Surprisingly enough, for me anyway, math is a big part of Commerce. Here I will be discussing how calculus plays a very important part in finding the elasticity of the economic curve.

[[File:Elastic.jpg]]

First of all, I would like to explain what elasticity actually is. In economics, elasticity is the ratio of the percent change in one variable to the percent change in another variable. Elasticity is used to measure how responsive one variable is to the other. It is said that if a variable has high elasticity then if that one variable is changed then this would impact the other greatly. On the other hand, if the variable is said to have a low elasticity then this means that if that same variable is changed then nothing or little with happen to the other variable. So, when is elasticity used? Mainly when looking at price elasticity of demand, price elasticity of supply, income elasticity of demand. Elasticity is essential in economics (according to professor Gateman). It is useful in understanding the marginal theory. For example, what happens to consumption if one more product increases its prices.
The formula for elasticity is:

Elasticity = (percentage change in Z) / (percentage change in Y)

From the get go, we see 2 variables that might have a relationship to each other. This already plays a big part in calculus.

Using some fairly basic calcululus, we can show that
(percentage change in Z) / (percentage change in Y) = (dZ / dY)*(Y/Z)

where dZ/dY is the partial derivative of Z with respect to Y. Thus we can calculate any elasticity through the formula:

'''Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)'''

Now… lets look at an example:

Demand is Q = 110 - 4P. What is price (point) elasticity at $5?

We saw that we can calculate any elasticity by the formula:
Y = (dQ / dp)*(P/Q)

That is the case in our demand equation of Q = 110 - 4P. Thus we differentiate with respect to P and get:
dQ/dP = -4

So we substitute dQ/dP = -4 and Q = 110 - 4P into our price elasticity of demand equation

Price elasticity of demand: = (dQ / dP)*(P/Q)

Price elasticity of demand: = (-4)*(P/(110-4P)

Price elasticity of demand: = -4P/(110-4P)

We want price elasticity at P = 5, so we substitute this into our price elasticity of demand equation:

= -4P/(110-4P)
= -20/90
= -2/9

Our price elasticity of demand is -2/9.

Since it is less than 1 > '''Demand is Price Inelastic'''

File:Elastic.jpg

2011-01-28T10:46:02Z

AndreaMameri:

User:AndreaMameri

2011-01-28T10:44:34Z

AndreaMameri: /* Calculus in economy */

===BIOGRAPHY===

'''HELLOOOOOOO''' everyone who is interested in my page!!!!!!

My name is Andrea Mameri, I'm from Ecuador. I was actually born I Ecuador and stayed there for 10 years of my life. Then I moved to Angola-Luanda where i spent 5 years living there. After this shocking change of my life, my father decided to go back to his roots in Brazil. I spent 2 years in the busy city of Sao Paulo after moving to Canada to continue my education.

Since my father is from Brazil, this means that i had dual citizenship. Therefore, I am part Ecuadorian and part Brazilian.
Which one do i call home? Where ever my family is.

I am currently in the Sauder School of Business

===Pythagorean theorem===

To refresh the memory and for me to complete the assignment, I will talk to you a little about the Pythagorean Theorem. I will try to make this fun. (Math is never fun, sry)

The Pythagorean Theorem can only be completed when working with right angle triangle. This means that one of the angles which make up a triangle is 90 degrees. The triangle is then composed of different lines. The longest line in the triangle is called the HYPOTENUSE; it is usually located right across the 90 degree angle. In the Pythagorean Theorem the HYPOTENUSE is represented by the letter C.

The Pythagorean Theorem is: <math>a^2+b^2=c^2</math>

The remaining two sides are represented by the letter A and the letter B. The order does not matter.

If a problem is given, the variables need to be plugged into the formula. If the HYPOTENUSE is given, this is plugged into the C, if one of the sides is given then this is plugged into A or B. Whichever side you are solving for, you make the equation equal that.

Example:
One side of a right angle triangle is 5 cm. The other side is 12 cm. Solve for the HYPOTENUSE.

<math>a^2 + b^2 = c^2</math>

<math>5^2 + 12^2 = c^2</math>

<math>25 + 144 = c^2</math>

<math>169 = c^2</math>

<math>c^2 = 169</math>

<math>c = √169</math>

<math>c = 13</math>

===Calculus in economy===

As I mentioned earlier on, the faculty that I am currently in is Commerce in the Sauder School of Business. Surprisingly enough, for me anyway, math is a big part of Commerce. Here I will be discussing how calculus plays a very important part in finding the elasticity of the economic curve.
First of all, I would like to explain what elasticity actually is. In economics, elasticity is the ratio of the percent change in one variable to the percent change in another variable. Elasticity is used to measure how responsive one variable is to the other. It is said that if a variable has high elasticity then if that one variable is changed then this would impact the other greatly. On the other hand, if the variable is said to have a low elasticity then this means that if that same variable is changed then nothing or little with happen to the other variable. So, when is elasticity used? Mainly when looking at price elasticity of demand, price elasticity of supply, income elasticity of demand. Elasticity is essential in economics (according to professor Gateman). It is useful in understanding the marginal theory. For example, what happens to consumption if one more product increases its prices.
The formula for elasticity is:

Elasticity = (percentage change in Z) / (percentage change in Y)

From the get go, we see 2 variables that might have a relationship to each other. This already plays a big part in calculus.

Using some fairly basic calcululus, we can show that
(percentage change in Z) / (percentage change in Y) = (dZ / dY)*(Y/Z)

where dZ/dY is the partial derivative of Z with respect to Y. Thus we can calculate any elasticity through the formula:

'''Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)'''

Now… lets look at an example:

Demand is Q = 110 - 4P. What is price (point) elasticity at $5?

We saw that we can calculate any elasticity by the formula:
Y = (dQ / dp)*(P/Q)

That is the case in our demand equation of Q = 110 - 4P. Thus we differentiate with respect to P and get:
dQ/dP = -4

So we substitute dQ/dP = -4 and Q = 110 - 4P into our price elasticity of demand equation

Price elasticity of demand: = (dQ / dP)*(P/Q)

Price elasticity of demand: = (-4)*(P/(110-4P)

Price elasticity of demand: = -4P/(110-4P)

We want price elasticity at P = 5, so we substitute this into our price elasticity of demand equation:

= -4P/(110-4P)
= -20/90
= -2/9

Our price elasticity of demand is -2/9.

Since it is less than 1 > '''Demand is Price Inelastic'''

User:AndreaMameri

2011-01-28T10:42:32Z

AndreaMameri: /* Calculus in economy */

===BIOGRAPHY===

'''HELLOOOOOOO''' everyone who is interested in my page!!!!!!

My name is Andrea Mameri, I'm from Ecuador. I was actually born I Ecuador and stayed there for 10 years of my life. Then I moved to Angola-Luanda where i spent 5 years living there. After this shocking change of my life, my father decided to go back to his roots in Brazil. I spent 2 years in the busy city of Sao Paulo after moving to Canada to continue my education.

Since my father is from Brazil, this means that i had dual citizenship. Therefore, I am part Ecuadorian and part Brazilian.
Which one do i call home? Where ever my family is.

I am currently in the Sauder School of Business

===Pythagorean theorem===

To refresh the memory and for me to complete the assignment, I will talk to you a little about the Pythagorean Theorem. I will try to make this fun. (Math is never fun, sry)

The Pythagorean Theorem can only be completed when working with right angle triangle. This means that one of the angles which make up a triangle is 90 degrees. The triangle is then composed of different lines. The longest line in the triangle is called the HYPOTENUSE; it is usually located right across the 90 degree angle. In the Pythagorean Theorem the HYPOTENUSE is represented by the letter C.

The Pythagorean Theorem is: <math>a^2+b^2=c^2</math>

The remaining two sides are represented by the letter A and the letter B. The order does not matter.

If a problem is given, the variables need to be plugged into the formula. If the HYPOTENUSE is given, this is plugged into the C, if one of the sides is given then this is plugged into A or B. Whichever side you are solving for, you make the equation equal that.

Example:
One side of a right angle triangle is 5 cm. The other side is 12 cm. Solve for the HYPOTENUSE.

<math>a^2 + b^2 = c^2</math>

<math>5^2 + 12^2 = c^2</math>

<math>25 + 144 = c^2</math>

<math>169 = c^2</math>

<math>c^2 = 169</math>

<math>c = √169</math>

<math>c = 13</math>

===Calculus in economy===

As I mentioned earlier on, the faculty that I am currently in is Commerce in the Sauder School of Business. Surprisingly enough, for me anyway, math is a big part of Commerce. Here I will be discussing how calculus plays a very important part in finding the elasticity of the economic curve.
First of all, I would like to explain what elasticity actually is. In economics, elasticity is the ratio of the percent change in one variable to the percent change in another variable. Elasticity is used to measure how responsive one variable is to the other. It is said that if a variable has high elasticity then if that one variable is changed then this would impact the other greatly. On the other hand, if the variable is said to have a low elasticity then this means that if that same variable is changed then nothing or little with happen to the other variable. So, when is elasticity used? Mainly when looking at price elasticity of demand, price elasticity of supply, income elasticity of demand. Elasticity is essential in economics (according to professor Gateman). It is useful in understanding the marginal theory. For example, what happens to consumption if one more product increases its prices.
The formula for elasticity is:
Elasticity = (percentage change in Z) / (percentage change in Y)

From the get go, we see 2 variables that might have a relationship to each other. This already plays a big part in calculus.
Using some fairly basic calcululus, we can show that
(percentage change in Z) / (percentage change in Y) = (dZ / dY)*(Y/Z)
where dZ/dY is the partial derivative of Z with respect to Y. Thus we can calculate any elasticity through the formula:
Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)

Now… lets look at an example:
Demand is Q = 110 - 4P. What is price (point) elasticity at $5?
We saw that we can calculate any elasticity by the formula:
Y = (dQ / dp)*(P/Q)
That is the case in our demand equation of Q = 110 - 4P. Thus we differentiate with respect to P and get:
dQ/dP = -4
So we substitute dQ/dP = -4 and Q = 110 - 4P into our price elasticity of demand equation:
Price elasticity of demand: = (dQ / dP)*(P/Q) Price elasticity of demand: = (-4)*(P/(110-4P) Price elasticity of demand: = -4P/(110-4P)
We want price elasticity at P = 5, so we substitute this into our price elasticity of demand equation:
= -4P/(110-4P) = -20/90 = -2/9
Our price elasticity of demand is -2/9.
Since it is less than 1 à Demand is Price Inelastic

User:AndreaMameri

2011-01-28T10:20:51Z

AndreaMameri:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-28T10:18:05Z

AndreaMameri: /* Homework */

{{
Infobox MATH110 Teams
| team name = Glarus
| member 1 = [[User:AndreaMameri|Andrea Mameri]]
| member 2 = Catherine Chen
| member 3 = Supreet Saran
| member 4 = Victoria Bass
}}

Hi.... My name is Andrea Mameri

phone number: 604-716-9520

email address: andreamameri@aim.com

skype name: andrea.mameri

You can find me on facebook as: Andrea Mameri

flabbergasted

Supreet Saran

lethargic

skype: supreetsaran

Hi everyone. I'm Victoria.

My email is bassvm@interchange.ubc.ca Yay!

BANANA!!!!!!

Hi! I'm Catherine.

fb and email: catherine chen (catherine1012_ling@hotmail.com)

Water Polo.

==Homework==

Homework 11: http://wiki.ubc.ca/Course:MATH110/003/Teams/Glarus/

Homework 12: http://wiki.ubc.ca/Course:MATH110/003/Teams/glarus/Homework_12

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T10:17:29Z

AndreaMameri:

[[Course:MATH110/003/Teams/Glarus/Homework 12|Homework 12]]

Homework #12
-----
'''What we have to do:'''

modify the function so that we can use it to model a real-life problem. We want to be able to control the following things:

Change the height of the horizontal asymptote on the right, we'll denote it by K.

Change the y-intercept to any number between 0 and K

Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical.

Information given:

[[File:Graph2.png]]

With the function P(t)= 1/1+e^-t we can modify it in a couple of ways. If we consider the function as P(t)= K/1+e^-t we can change the height of the horizontal asymptote on the right by setting K=whatever we want the horizontal asymptote on the right to be. The logic behind this involves considering the limit at +infinity. Horizontal asymptotes are limits at infinity. If we evaluate the limit at infinity for this function we find that it equals K.

Also, if we want to change the y intercept of the function then we can adjust A if we define the function as P(t)= 1/A+e^-t. At the y intercept t=0 so e^-t=1 so we get 1/A+1. This means we can adjust the y intercept to whatever we want because we just make A=whatever number we want minus 1.

We can now use this information to model something useful, like a population. We decided to model the population in Vancouver. For the sake of argument lets say that the carrying capacity of Vancouver is 1,000,000 people (a safe assumption since the biological definition of carrying capacity refers to the idea of the maximum population that an environment can support without habitat degradation and many people would argue that we're clearly already degrading the habitat and we're not yet at 1,000,000. If anything 1,000,000 would be well above carrying capacity but I digress...ANYWAY)

We want to find out in what year the population will reach 90% of its carrying capacity (in this case 900,000). According to trusty Wikipedia, the population of Vancouver was 578,041 people as of the 2006 census. Let's set that data point as our t=0. So our "Year 0" will be 2006 and so the y intercept will be 578,041 (the population at that time.)

P(t)= k/1+ae^(-rt)

k = Carrying capacity

a = Population at 0

r = Rate

t = x

We want to know when the population will reach 900,000 (90% of the carrying capacity). To determine this we can set P(t) as 900,000 and then evaluate for t.

To do this we need to figure out how much we need to shift our graph to the right so that the y intercept will be 578,041 and not halfway (500,000). To do this we have to find t when P(t)=578,041:

578,041= 10^6/1+e^-t

578,041 (1+e^-t)=10^6

1+e^-t = 10^6/578,041

e^-t=(10^6/578,041)-1

-t= ln [(10^6/578,041)-1]

-t=ln1.7-1

-t=0.7
-t=-0.3
t=0.3

So we need to shift our x coordinate 0.3 to the right for 578,041 to be our y intercept.

Now let's adjust the slope of the curved part by incorporating a specific rate of increase. According to worldometers.info the global population is increasing at a rate of 1.15%/year. Let's assume that since Vancouver is a smaller population to be drawing the percentage from that it is increasing slightly faster. Let's say that in 2006 the population was increasing at a rate of 2%/year. Since the population of Vancouver at that time was 578,041 the population would be increasing by 11,560.82 people that year (I know you can't have 0.82 of a person but let's just be accurate with our numbers and not round off at this point.) With our last variable r we have to determine what r is when the rate of change is 2%. To do this we have to a) find the derivative of the function so that we can model the rate of change b) set the derivative equal to 11,560.82 and solve for r (assuming t=0 because that's where P(t)=578,041)

P'(0)= [-(-re^(-rt+0.3)(10^6)]/(1+e^-rt+0.3)^2

11560=[-(-re^(-rt+0.3)(10^6)]/(1+e^-rt+0.3)^2

[(11560)(1+e^-rt+0.3)^2]/10^6= re^(-rt+0.3)

11560/10^6= (re^(-rt+0.3)/(1+e^-rt+0.3)^2

11560/10^6= [(r)(e^0.3)]/(1+e^0.3)^2

[(11560)(1+e^0.3)^2]/[(10^6)(e^0.3)]=r

0.047=r

So now our model is:

'''P(t)= 10^6/(1+e^(-0.047t+0.3))'''

We can determine when the population will reach 900,000 by evaluating P(900000) and solving for t.

900000=10^6/(1+e^(-0.047t+0.3))

We find that t=55.3 years
Since our t=0 at 2006 we add 55+2006 to determine that the population of Vancouver will reach 90% of its carrying capacity during 2061.

Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-28T10:15:53Z

AndreaMameri: /* Homework */

{{
Infobox MATH110 Teams
| team name = Glarus
| member 1 = [[User:AndreaMameri|Andrea Mameri]]
| member 2 = Catherine Chen
| member 3 = Supreet Saran
| member 4 = Victoria Bass
}}

Hi.... My name is Andrea Mameri

phone number: 604-716-9520

email address: andreamameri@aim.com

skype name: andrea.mameri

You can find me on facebook as: Andrea Mameri

flabbergasted

Supreet Saran

lethargic

skype: supreetsaran

Hi everyone. I'm Victoria.

My email is bassvm@interchange.ubc.ca Yay!

BANANA!!!!!!

Hi! I'm Catherine.

fb and email: catherine chen (catherine1012_ling@hotmail.com)

Water Polo.

==Homework==

Homework 10: http://wiki.ubc.ca/Course:MATH110/003/Teams/Glarus/

Homework 12: http://wiki.ubc.ca/Course:MATH110/003/Teams/glarus/Homework_12

Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-28T10:15:41Z

AndreaMameri: /* Homework */

{{
Infobox MATH110 Teams
| team name = Glarus
| member 1 = [[User:AndreaMameri|Andrea Mameri]]
| member 2 = Catherine Chen
| member 3 = Supreet Saran
| member 4 = Victoria Bass
}}

Hi.... My name is Andrea Mameri

phone number: 604-716-9520

email address: andreamameri@aim.com

skype name: andrea.mameri

You can find me on facebook as: Andrea Mameri

flabbergasted

Supreet Saran

lethargic

skype: supreetsaran

Hi everyone. I'm Victoria.

My email is bassvm@interchange.ubc.ca Yay!

BANANA!!!!!!

Hi! I'm Catherine.

fb and email: catherine chen (catherine1012_ling@hotmail.com)

Water Polo.

==Homework==

Homework 10: http://wiki.ubc.ca/Course:MATH110/003/Teams/Glarus/
Homework 12: http://wiki.ubc.ca/Course:MATH110/003/Teams/glarus/Homework_12

Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-28T10:13:58Z

AndreaMameri:

{{
Infobox MATH110 Teams
| team name = Glarus
| member 1 = [[User:AndreaMameri|Andrea Mameri]]
| member 2 = Catherine Chen
| member 3 = Supreet Saran
| member 4 = Victoria Bass
}}

Hi.... My name is Andrea Mameri

phone number: 604-716-9520

email address: andreamameri@aim.com

skype name: andrea.mameri

You can find me on facebook as: Andrea Mameri

flabbergasted

Supreet Saran

lethargic

skype: supreetsaran

Hi everyone. I'm Victoria.

My email is bassvm@interchange.ubc.ca Yay!

BANANA!!!!!!

Hi! I'm Catherine.

fb and email: catherine chen (catherine1012_ling@hotmail.com)

Water Polo.

==Homework==

http://wiki.ubc.ca/Course:MATH110/003/Teams/glarus/Homework_12

Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-28T10:12:11Z

AndreaMameri:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T10:11:48Z

AndreaMameri:

Homework #12
-----
'''What we have to do:'''

modify the function so that we can use it to model a real-life problem. We want to be able to control the following things:

Change the height of the horizontal asymptote on the right, we'll denote it by K.

Change the y-intercept to any number between 0 and K

Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical.

Information given:

[[File:Graph2.png]]

With the function P(t)= 1/1+e^-t we can modify it in a couple of ways. If we consider the function as P(t)= K/1+e^-t we can change the height of the horizontal asymptote on the right by setting K=whatever we want the horizontal asymptote on the right to be. The logic behind this involves considering the limit at +infinity. Horizontal asymptotes are limits at infinity. If we evaluate the limit at infinity for this function we find that it equals K.

Also, if we want to change the y intercept of the function then we can adjust A if we define the function as P(t)= 1/A+e^-t. At the y intercept t=0 so e^-t=1 so we get 1/A+1. This means we can adjust the y intercept to whatever we want because we just make A=whatever number we want minus 1.

We can now use this information to model something useful, like a population. We decided to model the population in Vancouver. For the sake of argument lets say that the carrying capacity of Vancouver is 1,000,000 people (a safe assumption since the biological definition of carrying capacity refers to the idea of the maximum population that an environment can support without habitat degradation and many people would argue that we're clearly already degrading the habitat and we're not yet at 1,000,000. If anything 1,000,000 would be well above carrying capacity but I digress...ANYWAY)

We want to find out in what year the population will reach 90% of its carrying capacity (in this case 900,000). According to trusty Wikipedia, the population of Vancouver was 578,041 people as of the 2006 census. Let's set that data point as our t=0. So our "Year 0" will be 2006 and so the y intercept will be 578,041 (the population at that time.)

P(t)= k/1+ae^(-rt)

k = Carrying capacity

a = Population at 0

r = Rate

t = x

We want to know when the population will reach 900,000 (90% of the carrying capacity). To determine this we can set P(t) as 900,000 and then evaluate for t.

To do this we need to figure out how much we need to shift our graph to the right so that the y intercept will be 578,041 and not halfway (500,000). To do this we have to find t when P(t)=578,041:

578,041= 10^6/1+e^-t

578,041 (1+e^-t)=10^6

1+e^-t = 10^6/578,041

e^-t=(10^6/578,041)-1

-t= ln [(10^6/578,041)-1]

-t=ln1.7-1

-t=0.7
-t=-0.3
t=0.3

So we need to shift our x coordinate 0.3 to the right for 578,041 to be our y intercept.

Now let's adjust the slope of the curved part by incorporating a specific rate of increase. According to worldometers.info the global population is increasing at a rate of 1.15%/year. Let's assume that since Vancouver is a smaller population to be drawing the percentage from that it is increasing slightly faster. Let's say that in 2006 the population was increasing at a rate of 2%/year. Since the population of Vancouver at that time was 578,041 the population would be increasing by 11,560.82 people that year (I know you can't have 0.82 of a person but let's just be accurate with our numbers and not round off at this point.) With our last variable r we have to determine what r is when the rate of change is 2%. To do this we have to a) find the derivative of the function so that we can model the rate of change b) set the derivative equal to 11,560.82 and solve for r (assuming t=0 because that's where P(t)=578,041)

P'(0)= [-(-re^(-rt+0.3)(10^6)]/(1+e^-rt+0.3)^2

11560=[-(-re^(-rt+0.3)(10^6)]/(1+e^-rt+0.3)^2

[(11560)(1+e^-rt+0.3)^2]/10^6= re^(-rt+0.3)

11560/10^6= (re^(-rt+0.3)/(1+e^-rt+0.3)^2

11560/10^6= [(r)(e^0.3)]/(1+e^0.3)^2

[(11560)(1+e^0.3)^2]/[(10^6)(e^0.3)]=r

0.047=r

So now our model is:

'''P(t)= 10^6/(1+e^(-0.047t+0.3))'''

We can determine when the population will reach 900,000 by evaluating P(900000) and solving for t.

900000=10^6/(1+e^(-0.047t+0.3))

We find that t=55.3 years
Since our t=0 at 2006 we add 55+2006 to determine that the population of Vancouver will reach 90% of its carrying capacity during 2061.

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T10:08:18Z

AndreaMameri:

Homework #12
-----
'''What we have to do:'''

modify the function so that we can use it to model a real-life problem. We want to be able to control the following things:

Change the height of the horizontal asymptote on the right, we'll denote it by K.

Change the y-intercept to any number between 0 and K

Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical.

Information given:

[[File:Graph2.png]]

With the function P(t)= 1/1+e^-t we can modify it in a couple of ways. If we consider the function as P(t)= K/1+e^-t we can change the height of the horizontal asymptote on the right by setting K=whatever we want the horizontal asymptote on the right to be. The logic behind this involves considering the limit at +infinity. Horizontal asymptotes are limits at infinity. If we evaluate the limit at infinity for this function we find that it equals K.

Also, if we want to change the y intercept of the function then we can adjust A if we define the function as P(t)= 1/A+e^-t. At the y intercept t=0 so e^-t=1 so we get 1/A+1. This means we can adjust the y intercept to whatever we want because we just make A=whatever number we want minus 1.

We can now use this information to model something useful, like a population. We decided to model the population in Vancouver. For the sake of argument lets say that the carrying capacity of Vancouver is 1,000,000 people (a safe assumption since the biological definition of carrying capacity refers to the idea of the maximum population that an environment can support without habitat degradation and many people would argue that we're clearly already degrading the habitat and we're not yet at 1,000,000. If anything 1,000,000 would be well above carrying capacity but I digress...ANYWAY)

We want to find out in what year the population will reach 90% of its carrying capacity (in this case 900,000). According to trusty Wikipedia, the population of Vancouver was 578,041 people as of the 2006 census. Let's set that data point as our t=0. So our "Year 0" will be 2006 and so the y intercept will be 578,041 (the population at that time.)

P(t)= k/1+ae^(-rt)

k = Carrying capacity

a = Population at 0

r = Rate

t = x

Our model for this population would then be:

'''''P(t)= 10^6/(578,040+e^-t)'''''

We want to know when the population will reach 900,000 (90% of the carrying capacity). To determine this we can set P(t) as 900,000 and then evaluate for t.

To do this we need to figure out how much we need to shift our graph to the right so that the y intercept will be 578,041 and not halfway (500,000). To do this we have to find t when P(t)=578,041:

578,041= 10^6/1+e^-t

578,041 (1+e^-t)=10^6

1+e^-t = 10^6/578,041

e^-t=(10^6/578,041)-1

-t= ln [(10^6/578,041)-1]

-t=ln1.7-1

-t=0.7
-t=-0.3
t=0.3

So we need to shift our x coordinate 0.3 to the right for 578,041 to be our y intercept.

Now let's adjust the slope of the curved part by incorporating a specific rate of increase. According to worldometers.info the global population is increasing at a rate of 1.15%/year. Let's assume that since Vancouver is a smaller population to be drawing the percentage from that it is increasing slightly faster. Let's say that in 2006 the population was increasing at a rate of 2%/year. Since the population of Vancouver at that time was 578,041 the population would be increasing by 11,560.82 people that year (I know you can't have 0.82 of a person but let's just be accurate with our numbers and not round off at this point.) With our last variable r we have to determine what r is when the rate of change is 2%. To do this we have to a) find the derivative of the function so that we can model the rate of change b) set the derivative equal to 11,560.82 and solve for r (assuming t=0 because that's where P(t)=578,041)

P'(0)= [-(-re^(-rt+0.3)(10^6)]/(1+e^-rt+0.3)^2

11560=[-(-re^(-rt+0.3)(10^6)]/(1+e^-rt+0.3)^2

[(11560)(1+e^-rt+0.3)^2]/10^6= re^(-rt+0.3)

11560/10^6= (re^(-rt+0.3)/(1+e^-rt+0.3)^2

11560/10^6= [(r)(e^0.3)]/(1+e^0.3)^2

[(11560)(1+e^0.3)^2]/[(10^6)(e^0.3)]=r

0.047=r

So now our model is:

P(t)= 10^6/(1+e^(-0.047t+0.3))

We can determine when the population will reach 900,000 by evaluating P(900000) and solving for t.

900000=10^6/(1+e^(-0.047t+0.3))

We find that t=55.3 years
Since our t=0 at 2006 we add 55+2006 to determine that the population of Vancouver will reach 90% of its carrying capacity during 2061.

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T10:04:50Z

AndreaMameri:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T10:04:14Z

AndreaMameri:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T10:00:22Z

AndreaMameri:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T09:53:40Z

AndreaMameri:

File:Graph2.png

2011-01-28T09:52:19Z

AndreaMameri: uploaded a new version of "File:Graph2.png"

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T09:52:03Z

AndreaMameri:

File:Graph2.png

2011-01-28T09:51:27Z

AndreaMameri: uploaded a new version of "File:Graph2.png"

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T09:50:00Z

AndreaMameri:

Homework #12

What we have to do:

----> modify the function so that we can use it to model a real-life problem. We want to be able to control the following things:

Change the height of the horizontal asymptote on the right, we'll denote it by K.

Change the y-intercept to any number between 0 and K

Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical.

Information given:

With the function P(t)= 1/1+e^-t we can modify it in a couple of ways. If we consider the function as P(t)= K/1+e^-t we can change the height of the horizontal asymptote on the right by setting K=whatever we want the horizontal asymptote on the right to be. The logic behind this involves considering the limit at +infinity. Horizontal asymptotes are limits at infinity. If we evaluate the limit at infinity for this function we find that it equals K.

Also, if we want to change the y intercept of the function then we can adjust A if we define the function as P(t)= 1/A+e^-t. At the y intercept t=0 so e^-t=1 so we get 1/A+1. This means we can adjust the y intercept to whatever we want because we just make A=whatever number we want minus 1.

We can now use this information to model something useful, like a population. We decided to model the population in Vancouver. For the sake of argument lets say that the carrying capacity of Vancouver is 1,000,000 people (a safe assumption since the biological definition of carrying capacity refers to the idea of the maximum population that an environment can support without habitat degradation and many people would argue that we're clearly already degrading the habitat and we're not yet at 1,000,000.

If anything 1,000,000 would be well above carrying capacity but I digress...ANYWAY) We want to find out in what year the population will reach 90% of its carrying capacity (in this case 900,000). According to trusty Wikipedia, the population of Vancouver was 578,041 people as of the 2006 census. Let's set that data point as our t=0. So our "Year 0" will be 2006 and so the y intercept will be 578,041 (the population at that time.) Our model for this population would then be:

'''''P(t)= 10^6/(578,040+e^-t)'''''

We want to know when the population will reach 900,000 (90% of the carrying capacity). To determine this we can set P(t) as 900,000 and then evaluate for t:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T05:47:05Z

AndreaMameri:

Homework #12

With the function P(t)= 1/1+e^-t we can modify it in a couple of ways. If we consider the function as P(t)= K/1+e^-t we can change the height of the horizontal asymptote on the right by setting K=whatever we want the horizontal asymptote on the right to be. The logic behind this involves considering the limit at +infinity. Horizontal asymptotes are limits at infinity. If we evaluate the limit at infinity for this function we find that it equals K.

Also, if we want to change the y intercept of the function then we can adjust A if we define the function as P(t)= 1/A+e^-t. At the y intercept t=0 so e^-t=1 so we get 1/A+1. This means we can adjust the y intercept to whatever we want because we just make A=whatever number we want minus 1.

We can now use this information to model something useful, like a population. We decided to model the population in Vancouver. For the sake of argument lets say that the carrying capacity of Vancouver is 1,000,000 people (a safe assumption since the biological definition of carrying capacity refers to the idea of the maximum population that an environment can support without habitat degradation and many people would argue that we're clearly already degrading the habitat and we're not yet at 1,000,000.

If anything 1,000,000 would be well above carrying capacity but I digress...ANYWAY) We want to find out in what year the population will reach 90% of its carrying capacity (in this case 900,000). According to trusty Wikipedia, the population of Vancouver was 578,041 people as of the 2006 census. Let's set that data point as our t=0. So our "Year 0" will be 2006 and so the y intercept will be 578,041 (the population at that time.) Our model for this population would then be:

'''''P(t)= 10^6/(578,040+e^-t)'''''

We want to know when the population will reach 900,000 (90% of the carrying capacity). To determine this we can set P(t) as 900,000 and then evaluate for t:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T05:46:29Z

AndreaMameri:

Homework #12

With the function P(t)= 1/1+e^-t we can modify it in a couple of ways. If we consider the function as P(t)= K/1+e^-t we can change the height of the horizontal asymptote on the right by setting K=whatever we want the horizontal asymptote on the right to be. The logic behind this involves considering the limit at +infinity. Horizontal asymptotes are limits at infinity. If we evaluate the limit at infinity for this function we find that it equals K.

Also, if we want to change the y intercept of the function then we can adjust A if we define the function as P(t)= 1/A+e^-t. At the y intercept t=0 so e^-t=1 so we get 1/A+1. This means we can adjust the y intercept to whatever we want because we just make A=whatever number we want minus 1.

We can now use this information to model something useful, like a population. We decided to model the population in Vancouver. For the sake of argument lets say that the carrying capacity of Vancouver is 1,000,000 people (a safe assumption since the biological definition of carrying capacity refers to the idea of the maximum population that an environment can support without habitat degradation and many people would argue that we're clearly already degrading the habitat and we're not yet at 1,000,000.

If anything 1,000,000 would be well above carrying capacity but I digress...ANYWAY) We want to find out in what year the population will reach 90% of its carrying capacity (in this case 900,000). According to trusty Wikipedia, the population of Vancouver was 578,041 people as of the 2006 census. Let's set that data point as our t=0. So our "Year 0" will be 2006 and so the y intercept will be 578,041 (the population at that time.) Our model for this population would then be:

''P(t)= 10^6/(578,040+e^-t)''

We want to know when the population will reach 900,000 (90% of the carrying capacity). To determine this we can set P(t) as 900,000 and then evaluate for t:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 12

2011-01-28T05:46:03Z

AndreaMameri: Created page with "Homework #12 With the function P(t)= 1/1+e^-t we can modify it in a couple of ways. If we consider the function as P(t)= K/1+e^-t we can change the height of the horizontal asy..."

Homework #12

With the function P(t)= 1/1+e^-t we can modify it in a couple of ways. If we consider the function as P(t)= K/1+e^-t we can change the height of the horizontal asymptote on the right by setting K=whatever we want the horizontal asymptote on the right to be. The logic behind this involves considering the limit at +infinity. Horizontal asymptotes are limits at infinity. If we evaluate the limit at infinity for this function we find that it equals K.

Also, if we want to change the y intercept of the function then we can adjust A if we define the function as P(t)= 1/A+e^-t. At the y intercept t=0 so e^-t=1 so we get 1/A+1. This means we can adjust the y intercept to whatever we want because we just make A=whatever number we want minus 1.
We can now use this information to model something useful, like a population. We decided to model the population in Vancouver. For the sake of argument lets say that the carrying capacity of Vancouver is 1,000,000 people (a safe assumption since the biological definition of carrying capacity refers to the idea of the maximum population that an environment can support without habitat degradation and many people would argue that we're clearly already degrading the habitat and we're not yet at 1,000,000. If anything 1,000,000 would be well above carrying capacity but I digress...ANYWAY) We want to find out in what year the population will reach 90% of its carrying capacity (in this case 900,000). According to trusty Wikipedia, the population of Vancouver was 578,041 people as of the 2006 census. Let's set that data point as our t=0. So our "Year 0" will be 2006 and so the y intercept will be 578,041 (the population at that time.) Our model for this population would then be:

""P(t)= 10^6/(578,040+e^-t)""

We want to know when the population will reach 900,000 (90% of the carrying capacity). To determine this we can set P(t) as 900,000 and then evaluate for t:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-24T16:14:01Z

AndreaMameri:

Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-24T16:11:35Z

AndreaMameri:

{{
Infobox MATH110 Teams
| team name = Glarus
| member 1 = [[User:AndreaMameri|Andrea Mameri]]
| member 2 = Catherine Chen
| member 3 = Supreet Saran
| member 4 = Victoria Bass
}}

Hi.... My name is Andrea Mameri

phone number: 604-716-9520

email address: andreamameri@aim.com

skype name: andrea.mameri

You can find me on facebook as: Andrea Mameri

flabbergasted

Supreet Saran

skype: supreetsaran

Hi everyone. I'm Victoria.

My email is bassvm@interchange.ubc.ca Yay!

BANANA!!!!!!

Hi! I'm Catherine.

fb and email: catherine chen (catherine1012_ling@hotmail.com)

Water Polo.

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 10

2011-01-19T15:50:06Z

AndreaMameri:

[http://wiki.ubc.ca/Course:MATH110/003/Teams/Glarus/Homework11 Homework 11]

'''THIRD PART'''
= =

Homework Question:

Model: y= 7x-40

The model is specified to be linear so we know that it will follow the formula of y=mx+b. We also know that the marginal cost is $7/unit. Since x is the # of units we know that 7x describes part of our cost. Meaning we now have y=7x+b. When we produce 20 items (when x = 20) our total cost is $100. This gives us 100= 7(20)+b. We can then solve for b and find that b=-40.

For 150 items our model predicts a cost of $1010. We find this by:

y=7(150)-40

y=1010

This means that the average cost per item increases as production levels increase. We find this through the following logic:

When we produced 20 items our cost was $100 (x=20, y=100) this means that the average cost per item was $5 (100/20). When we produced 150 items our cost was $1010 (x=150, y=1010) this means that the average cost per item was $6.73 (1010/150)

In consideration of other models, this model would be an example of one where average cost increases as production increases (as we have just shown.)

= =
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

[[File:Graph.png]]

Example: For every book that is purchased the price is going to be less than the overall (average) price of all the books. Eventually, the graph is going to intersect the average cost curve. But in our case that does not happen. Average cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q).

The average cost diminishes as production increases- the slope in this case is negative, which means that the marginal cost is negative.

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 10

2011-01-19T10:10:46Z

AndreaMameri:

[http://wiki.ubc.ca/Course:MATH110/003/Teams/Glarus/Homework11 Homework 11]

'''THIRD PART'''
= =

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

[[File:Graph.png]]

Example: For every book that is purchased the price is going to be less than the overall (average) price of all the books. Eventually, the graph is going to intersect the average cost curve. But in our case that does not happen. Average cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q).

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 10

2011-01-19T10:10:35Z

AndreaMameri:

[http://wiki.ubc.ca/Course:MATH110/003/Teams/Glarus/Homework11 Homework 11]

'''THIRD PART'''
= = =

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

[[File:Graph.png]]

Example: For every book that is purchased the price is going to be less than the overall (average) price of all the books. Eventually, the graph is going to intersect the average cost curve. But in our case that does not happen. Average cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q).

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 10

2011-01-19T10:10:23Z

AndreaMameri:

[http://wiki.ubc.ca/Course:MATH110/003/Teams/Glarus/Homework11 Homework 11]

'''THIRD PART'''
= = = =

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

[[File:Graph.png]]

Example: For every book that is purchased the price is going to be less than the overall (average) price of all the books. Eventually, the graph is going to intersect the average cost curve. But in our case that does not happen. Average cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q).

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 10

2011-01-19T10:08:39Z

AndreaMameri:

[http://wiki.ubc.ca/Course:MATH110/003/Teams/Glarus/Homework11 Homework 11]

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

[[File:Graph.png]]

Example: For every book that is purchased the price is going to be less than the overall (average) price of all the books. Eventually, the graph is going to intersect the average cost curve. But in our case that does not happen. Average cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q).

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 10

2011-01-19T10:07:21Z

AndreaMameri:

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

[[File:Graph.png]]

Example: For every book that is purchased the price is going to be less than the overall (average) price of all the books. Eventually, the graph is going to intersect the average cost curve. But in our case that does not happen. Average cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q).

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 10

2011-01-19T10:00:55Z

AndreaMameri:

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

[[File:Graph.png]]

Course:MATH110/Archive/2010-2011/003/Teams/Glarus/Homework 10

2011-01-19T10:00:17Z

AndreaMameri: Created page with "File:Graph.png"

[[File:Graph.png]]

File:Graph.png

2011-01-19T09:59:49Z

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2011-01-19T09:59:34Z

AndreaMameri: uploaded a new version of "File:Graph.png": Reverted to version as of 09:55, 19 January 2011

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2011-01-19T09:59:19Z

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2011-01-19T09:55:02Z

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Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-19T09:46:21Z

AndreaMameri:

{{
Infobox MATH110 Teams
| team name = Glarus
| member 1 = [[User:AndreaMameri|Andrea Mameri]]
| member 2 = Catherine Chen
| member 3 = Supreet Saran
| member 4 = Victoria Bass
}}

Hi.... My name is Andrea Mameri

phone number: 604-716-9520

email address: andreamameri@aim.com

skype name: andrea.mameri

You can find me on facebook as: Andrea Mameri

Supreet Saran

skype: supreetsaran

Hi everyone. I'm Victoria.

My email is bassvm@interchange.ubc.ca Yay!

Hi! I'm Catherine.

fb and email: catherine chen (catherine1012_ling@hotmail.com)

Course:MATH110/Archive/2010-2011/003/Teams/Glarus

2011-01-19T09:46:04Z

AndreaMameri:

{{
Infobox MATH110 Teams
| team name = Glarus
| member 1 = [[User:AndreaMameri|Andrea Mameri]]
| member 2 = Catherine Chen
| member 3 = Supreet Saran
| member 4 = Victoria Bass
}}

Hi.... My name is Andrea Mameri

phone number: 604-716-9520

email address: andreamameri@aim.com

skype name: andrea.mameri

You can find me on facebook as: Andrea Mameri

Supreet Saran

skype: supreetsaran

Hi everyone. I'm Victoria. My email is bassvm@interchange.ubc.ca Yay!

Hi! I'm Catherine.

fb and email: catherine chen (catherine1012_ling@hotmail.com)

File:Graph.png

2011-01-19T09:43:17Z

AndreaMameri: uploaded a new version of "File:Graph.png"