Question

A brand-new vehicle is bought this year for $35,000. This vehicle model is expected to depreciate by about 12% in resale value annually. Find a model for the resale value of this vehicle after x years and use this model to estimate its resale value by year 10.

Answer 1

The model for the resale value of the vehicle is

`A=35000(0.88)^x`

where A is the resale value of the car after x years in dollar.

The resale value of the car after 10 years is $9747.53.

Explanation:

Given that, a brand new vehicle is bought this year for $35,000.

This vehicle model is expected to depreciate by about 12 % in resale value annually.

We use the following formula to find the value of car after t year,

`A=P(1+r)^t`

A= the value of car after t years

P= initial amount of the car

r = rate

t = time

since the value of decreases so, r= -12%,t=x years, P=$35,000

`A=35000(1-0.12)^x`

`\Rightarrow A=35000(0.88)^x`

where A is the resale value of the car after x years in dollar.

The model for the resale value of the vehicle is

`A=35000(0.88)^x`

To find the resale value of car after 10 years, we put x=10 in the above model equation

`A=35000(0.88)^(10)`

=$9747.53

The resale value of the car after 10 years is $9747.53.