Science:Math Exam Resources/Courses/MATH102/December 2017/Question 10 (a)

MATH102 December 2017

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Question 10 (a)

An animal foraging in a food patch has a net energy gain of ${\textstyle f(t)}$ by the time it has been foraging for ${\textstyle t}$ min (where ${\textstyle t}$ is nonnegative and ${\textstyle f(0)=0}$). (a) Let ${\textstyle A(t)}$ be the average net energy gained per unit time. Write down an expression for ${\textstyle A(t)}$ in terms of ${\textstyle f(t)}$ and ${\textstyle t}$. ${\textstyle A(t)=}$

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
Consider the average over the interval $(0,t)$. Find the change of a function value and the change of a time in the interval first.

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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. From time ${\textstyle 0}$ to time ${\textstyle t}$, the net energy gain is ${\textstyle f(t)=f(t)-f(0)}$. Therefore the average is $$A(t)={\dfrac {f(t)}{t}}.$$ Answer: ${\textstyle {\color {blue}A(t)={\dfrac {f(t)}{t}}}}$.