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

MATH102 December 2017

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### Question 12 (d)

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.

(d) Approximately how old is Dione? You may assume that Dione had no craters on its surface when it first formed. Your answer here should also be a simplified rational number (use the same linear approximation again).

Remark: you can earn partial credit for this part by expressing the age in terms of $k$ , even if you did not find the rational approximation in part (c).

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