The value of a car depreciates each year Suppose that you pu

The value of a car depreciates each year. Suppose that you purchased a car for $21,000 and the value of the car depreciates by 12% each year.

Determine the following: Initial value of the car: dollars

A.) 1-year growth factor:

B.) 1-year percent change: %

C.) Define a function f f that determines the value of the car in terms of the number of years since the car was purchased, x

D.) Determine the value of the car 8 years after it was purchased. (You may round your answer to the nearest penny).

Solution

A) 1-year growth factor=(1-(12/100))

1-year growth factor=1-0.12

1-year growth factor=0.88

B)1-year percent change: 12%

C)f (x)=21000(1-(12/100))^x

f (x)=21000(1-0.12)^x

f (x)=21000(0.88)^x

D)value of the car 8 years after it was purchased is f(8)=21000(0.88)⁸

. f(8)=7552.33

value of the car 8 years after it was purchased =$ 7552.33