Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (d)
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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 craterfree 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 , even if you did not find the rational approximation in part (c). 
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Hint 

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let the age be . We need to solve the equation : By the approximation in part (c), we have By the linear approximation, Therefore, In other words, Dione is approximate years old.
Answer: the age of Dione is approximately years. 