Question

After a new $28,000 car is driven off the lot, it begins to depreciate at a rate of 18.9% annually.Which function describes the value of the car after t years?

Answer 1

It begins to depreciate at a rate of 18.9% annually. This means that the rate at which the value is decreasing is exponential. We would apply the formula for exponential decay which is expressed as

`y=b(1-r)^t`

Where,

y represents the value of the car after t years.

t represents the number of years.

b represents the initial value of the car.

r represents the rate of depreciation.

Given

`\begin{gathered} P=\text{ \$28000} \\ r=18.9\%=(18.9)/(100)=0.189 \\ \end{gathered}`

Therefore,

`\begin{gathered} y=28000(1-0.189)^t \\ \therefore y=28000(0.811)^t \end{gathered}`

Where C(t) represents y,

Therefore, the function becomes

`C(t)=28000(0.811)^t`

Hence, the function that describes the value of the car after t years is

`C(t)=28000(0.811)^t\text{ (OPTION 1)}`