Question

Find the value of the car after 7 years and after 12 years. Round your answer to the nearest dollar as necessary

Answer 1

Given:

The value of cat v(t) that is t years old is given by the exponential function.

`v(t)=24,500(0.80)^t`

Required:

Find the value of the car after 7 years and after 12 years.

Step-by-step explanation:

Substitute t = 7 in the given function.

`\begin{gathered} v(7)=24,500(0.80)^7 \\ v(7)=24,500*0.2097152 \\ v(7)=5138.0224 \\ v(7)=5183.02 \end{gathered}`

After 7 years the value of the car is $5138.02

Substitute t = 12 in the given function.

`\begin{gathered} v(12)=24,500(0.80)^(12) \\ v(12)=24,500*0.0687194767 \\ v(12)=1683.62717 \\ v(12)\approx1683.62 \end{gathered}`

After 7 years the value of the car is $ 1683.62

Final answer:

The value of the car after 7 years and 12 years is $5138.02 and $ 1683.62.