Question

The dollar value v (t) of a certain car model that is t years old is given by the following exponential function.J (8L^ * 0)000^ 4 ZE=(1) LambdaFind the initial value of the car and the value after 12 years.Round your answers to the nearest dollar as necessary.

Answer 1

Given the following question:

`v(t)=32000(0.78)^t`

Part A:

The initial value of the car is 32000, speaking how it's the original amount which is the first value we use to find the product between 0.78 and 32000.

Your initial value is 32,000

Part B:

To find the amount after 12 years.

`\begin{gathered} v(t)=32000(0.78)^t \\ t=12 \\ v(t)=32000(0.78)^(12) \\ 0.78^(12)=0.0507148602 \\ v(t)=32000(0.0507148602) \\ 32000(0.0507148602)=1622.87553 \\ 1622.87553 \\ 5=5 \\ 1622.88 \\ \text{ The value of the car after 12 years is 1622.88} \end{gathered}`