Science:Math Exam Resources/Courses/MATH101/April 2011/Question 05 (c)

MATH101 April 2011

  •  Q1 (a)  •  Q1 (b)  •  Q1 (c)  •  Q1 (d)  •  Q1 (e)  •  Q1 (f)  •  Q1 (g)  •  Q1 (h)  •  Q1 (i)  •  Q1 (j)  •  Q2 (a)  •  Q2 (b)  •  Q3 (a)  •  Q3 (b)  •  Q4 (a)  •  Q4 (b)  •  Q4 (c)  •  Q4 (d)  •  Q5 (a)  •  Q5 (b)  •  Q5 (c)  •  Q6 (a)  •  Q6 (b)  •  Q7  •  Q8  •  

   Other MATH101 Exams

  •  April 2011  •  April 2010  •  April 2009  •  April 2008  •  April 2007  •  April 2005  •  April 2006  •  April 2012  •  April 2013  •  April 2014  •  April 2015  •  April 2016  •  April 2018  •  April 2017  •  

Question 05 (c)

Bird-Bath and Beyond Incorporated is famous for its Quetzal attracting bird-feeder solution made from water, honey and cane-sugar. To make their solution, both honey and a cane-sugar solution are poured into a 200 L mixing tank. The honey is poured in at a rate of 1 L per minute while the sugar solution is poured in at 9 L per minute. Note that 1 L of honey contains 1 kg of sugar, while the cane-sugar solution contains 100g of sugar per L. Unfortunately today there is a problem with the mixing tank. It was thoroughly cleaned and is initially filled with pure water, but main valve was broken and the water cannot be drained. When the mixing process is started, the honey and sugar-solutions are poured into the tank, and the excess fluid flows out of an emergency valve at 10 L per minute and onto the floor. You should assume that the solutions mix immediately and thoroughly in the tank. (c) The bird feeder solution can only be sold if there is at least 30 kg of sugar in the 200 L tank. If the flow of sugar solution and honey is switched off after 20 minutes, can the result be sold?

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Is S(20) larger than 30?

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work. If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work. If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.

Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Pluggin in t=20 we obtain ${\begin{aligned}S(20)&=20\left(1.9-1.9e^{-20/20}\right)\\&=20\left(1.9-{\frac {1.9}{e}}\right)\\&=38-{\frac {38}{e}}\\&\leq 38-10<30.\end{aligned}}$ Remember that $\displaystyle e\approx 2.7$ and hence ${\frac {38}{e}}>10.$ That means that after 20 minutes there is less than 30kg of sugar in the tank. Thus the solution cannot be sold.

Click here for similar questions

MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Population dynamics, Pages using DynamicPageList3 parser function, Pages using DynamicPageList3 parser tag