Question

Which amount is closest to the value of the car 10 years after it was purchased?

Answer 1

Divide each term to determine the common ratio

`\begin{gathered} (14450)/(17000)=0.85 \\ (12200)/(14450)=0.844 \\ (10400)/(12200)=0.85 \\ (8900)/(10400)=0.855 \end{gathered}`

The common ratio for the succeding years is approximately 0.85.

Use the exponential function using the initial value of 17000, and base of 0.85 to determine approximate car value after 10 years

`\begin{gathered} y=17000(0.85)^(t-1) \\ y=17000(0.85)^(10-1) \\ y=17000(0.85)^9 \\ y=3,937.48 \end{gathered}`

Rounding to the nearest thousand of dollars. The closest value of the car after 10 years is $4000.