Answer
$y=12500\left(0.91\right)^x$, where $x$ is the time in years
The value of the car after $5$ years is $\$7,800.40$.
Work Step by Step
Recall:
The exponential function $y=c \cdot b^x$ involves:
(1) an exponential growth if $b\gt1$.
(2) an exponential decay if $0\lt b \lt1$.
The car depreciates $9\%$ per year.
This means that the base will be:
\begin{align*}
b&=1-9\%\\
b&=1-0.09\\
b&=0.91
\end{align*}
The given function has an initial value (which is $c$) of $12,500$.
Thus, the function that models the situation, where $x$ is the number of years, is:
$$y=12500\left(0.91\right)^x$$
To find the value of the car after $5$ years, substitute $5$ to $x$ to obtain:
\begin{align*}
y&=12500\left(0.91\right)^5\\
y&\approx7,800.40
\end{align*}
Thus, the car will be worth $\$7,800.40$ after $5$ years.
