The value of a particular item can be modeled by P(t) = P0(a)t where P is in dollars and t is the number of years since the item was purchased. Suppose the value of the item increases 5% each year and the item was purchased for $20. (a) Write a formula for P(t) according to the model. P(t) = (b) How fast is the value of the item increasing when t = 25 years? Round your answer to two decimal places.

(1) Answers

a.) P(t) = 20(1.05)^t b.) P'(t) = P(t)20ln(1.05) P'(25) = P(25)20ln(1.05) P'(25) = 20(1.05)^25 * 20ln(1.05) = 66.09 Therefore,the value of the item increases at the rate of $66.09 when t = 25 years.

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