Question

Which function represents the value of the car after t years?

Answer 1

Given:

The value of car = $ 21000.

Rate of depreciation = 15 %.

Depreciation is an exponential decay function.

Consider the exponential decay function.

`f(x)=a(1-r)^t`

where a is the initial value and r is the rate of percentage.

Substitute a=21000 and r=15 %, we get

`f(x)=21000(1-(15)/(100))^t^{}`

`f(x)=21000((100)/(100)-(15)/(100))^t`

`f(x)=21000((100-15)/(100))^t`

`f(x)=21000((85)/(100))^t`

`f(x)=21000(0.85)^t`

The function that represents the value of the car after t years is

`f(x)=21000(0.85)^t`