Science:Math Exam Resources/Courses/MATH102/December 2015/Question 06
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Question 06 

If we assume that the amount of food gained in a food patch during time is
then (a) The total amount of food in the patch is . (b) Getting food from the patch is initially a slow process but then it speeds up for a while. (c) It takes a time to get all the energy out of the patch. (d) It takes a time to get all the energy out of the patch. (e) There is unlimited energy in the patch. 
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 

This is a Hill function. If you understand the behaviour of Hill functions, this problem can be easily solved. If not, think about how statements (a), (b), (c), (d), and (e) can be rephrased in terms of the asymptotes of . 
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.

Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. This solution will use the theory of Hill functions. An introduction can be found in this video. You may also want to view the second solution presented below. 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. Solution 2: The statements (a), (b), (c), (d), and (e) can all be phrased in terms of and : 