Question

The dollar value v (t) of a certain car model that is t years old given by the following exponential function. v(t) =19,900(0.90) tFind the initial value if the car and the value after 12 years. Round your answers to the nearest dollar as necessary.

Answer 1

Given

`v(t)=19,900(0.90)^t`

Procedure

Initial value

`\begin{gathered} v(0)=19,900(0.90)^0 \\ v(0)=19,900 \end{gathered}`

19,900 initial value of the car

value after 12 years

`\begin{gathered} v(12)=19,900(0.90)^(12) \\ v(12)=19,900\cdot0.2824 \\ v(12)=5,620.34 \end{gathered}`

$5,620.34 value of the car after 12 years