Question

5. Landon bought a new car for $16,000 and it depreciates 4.5% every year. Write a function that describes

the value, C(t), of the car after 5 years.

Answer 1

The value C(t) of the car after 5 years is $12709.

Explanation:

Given that Landon bought a new car for $16,000 and it depreciates 4.5% every year.

To find the value C(t) of the car after 5 years:

Initial value
`C(0)= $16,000`

Depreciation rate is
`r=(4.5)/(100)`

∴ r=0.045

Period , t=5 years

`C(t)=C(0)(1-r)^t`

Substitute the values we get

`C(5)=16000(1-0.045)^5`

`=16000(0.955)^5`

`=16000(0.7943)`

∴
`C(5)=12708.8`

The value C(t) of the car after 5 years is $ 12709