Answer
Function that models the car's expected value after $x$ years:
$\text{FV}=25000(0.85)^x$
Expected value after $5$ years:
$\$11,092.63$
Work Step by Step
Recall:
Depreciation Formula
The future value $\text{FV}$ of a physical property that depreciates in value over time is given by the formula:
$$\text{FV}=P(1-r)^x$$
where
$P$ = present value
$r$ = depreciation rate per year
$x$ = time in years
Thus, the future value of a car worth $\$25,000$ at the moment and depreciates $r\%$ per year will be modeled by the formula:
$$\text{FV} = 25,000\left(1-r\right)^x$$
The value of the car after one year is $\$21,250$.
Substitute $1$ to $x$ and $21250$ to $\text{FV}$ to find the value of $r$:
\begin{align*}
21250& = 25000\left(1-r\right)^1\\\\
21250& = 25000\left(1-r\right)\\\\
\frac{21250}{25000}& = \frac{25000\left(1-r\right)}{25000}\\\\
0.85 &=1-r\\\\
0.85 - 1 &= -r\\
-0.15&= -r\\
0.15 &= r
\end{align*}
Thus, the exponential function that models the car's expected value ($\text{FV}$) after $x$ years is:
\begin{align*}
\text{FV}&=25,000(1-0.15)^x\\
\text{FV}&=25000(0.85)^x
\end{align*}
The estimated value of the car after $5$ years can be found by substituting $5$ to $x$:
\begin{align*}
\text{FV}&=25,000(0.85)^5\\
&\approx 11,092.63
\end{align*}
