Question

Brianna bought her car for $39,367. It is expected to depreciate an average of 22%each year during the first 9 years.What will the approximate value of her car be in 9 years? Round answer to thenearest dollar.

Answer 1

Let's assume we have a base value of K and we are told that it depreciates an average of p% each year. The value V(t) after t years is given by the following exponential function:

`V(t)=K\cdot(1-(p)/(100))^t`

In this case K is the original value of the car $39367, p is the percentage of depreciation i.e. 22. Then the value of the car bought by Brianna t years after she bought it is:

`V(t)=39367\cdot(1-(22)/(100))^t=39367\cdot0.78^t`

Then the approximate value in 9 years will be V(9):

`V(9)=39367\cdot0.78^9=4207.11`

We need to round it to the nearest dollar so the answer is $4207.