Science:Math Exam Resources/Courses/MATH100/December 2010/Question 02 (b)
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Question 02 (b) 

FullSolution Problems. In questions 28, justify your answers and show all your work. If a box is provided, write your final answer there. Simplification of answers is not required unless explicitly requested. When an apple is taken from a refrigerator, its temperature is . After 30 minutes in a room, its temperature is . Find the temperature of the apple 90 minutes after it is taken from the refrigerator, expressed as an integer number of degrees Celsius. 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

The simplest differential equation we can solve for is
which gives the solution
How can we make our current equation look like this? 
Hint 2 

Set
Then use the hint to get the differential equation. 
Hint 3 

The last step is to solve for k using the given information. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

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. Proceeding as in the hints, let
Then, Newton's law of cooling reads
Solving this differential equation gives
In terms of T and using the initial condition , we have
After 30 minutes, we know and so
Solving for k by isolating and taking logarithms gives
We want to find the temperature after 90 minutes and so
and thus degrees celsius 