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.

Question

Poncho

Mathematics

25 March, 12:53

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.

+3

Answers (1)

Know the Answer?

Sloane Sparks · Answer 1

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.