Answer
$y=50\left(1.03\right)^x$, where $x$ represents the time in years.
The value of the card after $5$ years is around $\$57.96$.
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 card value increases by $3\%$ per year.
This means that the base will be:
\begin{align*}
b&=1+3\%\\
b&=1+0.03\\
b&=1.03
\end{align*}
The given function has an initial value (which is $c$) of $50$.
Thus, the function that models the situation, where $x$ is the number of years, is:
$$y=50\left(1.03\right)^x$$
To find the value of the car after $5$ years, substitute $5$ to $x$ to obtain:
\begin{align*}
y&=50\left(1.03\right)^5\\
y&\approx57.96
\end{align*}
Thus, the card will be worth $\$57.96$ after $5$ years.
