Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (c)
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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 craterfree 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! 
Hint 

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.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By the Hint, for , , we have , , . Hence the linear approximation is We recall from part (b) that By the linear approximation, we have Answer: . 