Question

Evaluate an exponential function that models a real world problem

Answer 1

• Initial value: $26,000.

,

• Value after 12 years: $1,319

Explanation:

The value of a car model that is t years old is given by the function:

`v(t)=26,000(0.78)^t`

(a)The Initial Value

At the initial point of purchase, the value of t=0.

`\begin{gathered} v(0)=26,000(0.78)^0 \\ =26000*1 \\ =\$26,000 \end{gathered}`

The initial value is $26,000.

(b)Value after 12 years

When t=12:

`\begin{gathered} v(12)=26,000(0.78)^(12) \\ =1318.6 \\ =\$1,319 \end{gathered}`

The value of the car after 12 years is $1,319 (correct to the nearest dollar).