# Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (c)

MATH102 December 2017
Other MATH102 Exams

### 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 ${\displaystyle f(x)=\ln(x)}$ at ${\displaystyle x=1}$ and use it to estimate ${\displaystyle k}$ by linear approximation. Your answer should be a rational number.

Remark: you can solve this part without solving the other parts.

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