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

MATH102 December 2017

  •  Q1  •  Q2  •  Q3  •  Q4  •  Q5  •  Q6  •  Q7 (a)  •  Q7 (b)  •  Q7 (c)  •  Q8  •  Q9 (a)  •  Q9 (b)  •  Q9 (c)  •  Q10 (a)  •  Q10 (b)  •  Q10 (c)  •  Q10 (d)  •  Q11 (a)  •  Q11 (b)  •  Q12 (a)  •  Q12 (b)  •  Q12 (c)  •  Q12 (d)  •  Q13 (a)  •  Q13 (b)  •  Q13 (c)  •  Q13 (d)  •  Q14 (a)  •  Q14 (b)  •  Q15 (a)  •  Q15 (b)  •  Q16  •  

   Other MATH102 Exams

  •  December 2014  •  December 2011  •  December 2012  •  December 2013  •  December 2016  •  December 2015  •  

Question 10 (b)

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 ${\textstyle f(0)=0}$). (b) For any positive time ${\textstyle t}$, what is the geometric interpretation of the function ${\textstyle A(t)}$, as it appears on the graph of ${\textstyle f(t)}$? Circle the letter corresponding to your choice. A. It is the slope of the secant line from ${\textstyle (0,0)}$ to ${\textstyle (t,f(t))}$. B. It is the slope of the tangent line at ${\textstyle (t,f(t))}$. C. It is the tangent line to ${\textstyle f(t)}$ that goes through the origin. D. It is the steepest secant line on ${\textstyle f(t)}$.

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
Recall that ${\textstyle f(0)=0}$. Then, we can write $${\dfrac {f(t)}{t}}={\dfrac {f(t)-f(0)}{t-0}}.$$

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. Since ${\textstyle f(0)=0}$, we can write $$A(t)={\dfrac {f(t)}{t}}={\dfrac {f(t)-f(0)}{t-0}}.$$ This is the slope of the secant line joining ${\textstyle (0,0)}$ and ${\textstyle (t,f(t))}$. Answer: ${\textstyle {\color {blue}A}}$.