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 •
Question 12 (c)
The age of a solid planet can be estimated by calculating the fraction of the
surface of the planet that is free of meteor impact craters. Assume that the
rate at which the crater-free area decreases is proportional to that area itself.
(c) Find the tangent line to at and use it to estimate
by linear approximation. Your answer should be a rational number.
Remark: you can solve this part without solving the other parts.
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!
Recall that the linear approximation of at is .
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.
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By the Hint, for , , we have , , . Hence the linear approximation is
We recall from part (b) that
By the linear approximation, we have