Question

The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.v(t) = 19, 900 * (0.84) ^ tRound your answers to the nearest dollar as necessary.Find the initial value of the car and the value after 11 years.

Answer 1

Given

`v(t)=19900(0.84)^t`

a) The car has its original (initial) value when no time has passed since it was bought; in other words t=0. Then,

`\text{ initial value: }v(0)=19900(0.84)^0=19900*1=19900`

The initial value is 19900.

b) After 11 years, t=11; then,

`\begin{gathered} v(11)=19900(0.84)^(11)=2923.64894... \\ \Rightarrow v(11)\approx2924 \end{gathered}`

Rounded to the nearest tenth, the second answer is 2924