Question

A national study found that a car's value decreases by 15 percent annually. If the car was purchased for 66,000. How much will the car be worth in 10 years?

Answer 1

$12,993.71

Explanation:

First raise .85 to the 10th power to get

A(t) = 66,000(.1968744043)

and then multiply to get

A(t) = $12,993.71

Answer 2

$12,993.71

Explanation:

The formula we want for this is exponential decay which is

`A(t)=a(1-r)^t`

where A(t) is the value of the car after the depreciation, a is the initial value of the car, r is the interest rate at which it depreciates in decimal form, and t is the time in years. We have everything we need to fill in to solve for A(t):

`A(t)=66,000(1-.15)^(10)`

We will do some simplifying first:

`A(t)=66,000(.85)^(10)`

First raise .85 to the 10th power to get

A(t) = 66,000(.1968744043)

and then multiply to get

A(t) = $12,993.71