Answer
$y=3^x+2$
Work Step by Step
The general formula for an exponential function can be defined as:
$y=Ca^x+b~~~(1)$
Where we have the horizontal asymptote $=b$.
So, in our case, we have:
$y=Ca^x+2~~~(2)$
Plug in $x=0$ and $y=3$ to compute the values of $C$ and $a$.
$Ca^0+2=3\\
C+2=3\\C=1 $
Thus, the equation (2) becomes: $y=a^x+2$
Now, plug in $x=1$ and $y=5$ to compute the values of $C$ and $a$.
$y=a^x+2\\ 5=a+2\\
5-2=a\\
a=3$
Thus, the required equation is $y=3^x+2$
