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13 July, 21:47

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.

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Answers (1)
  1. 14 July, 00:04
    0
    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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