Answer
$y=3^x+2$
Work Step by Step
The general formula for an exponential function: $Ca^x+b=y$.
The horizontal asymptote is $b$.
With $b=2$, then the tentative equation is $Ca^x+2=y$.
We plug in $x$ and $y$ values of each of the $2$ known points $(0,3)$ and $(1,5)$ to find the values of $C$ and $a$.
For $(0, 3)$:
$Ca^0+2=3\\
C+2=3\\
C=3-2\\
C=1. $
Thus, $y=1\cdot a^x+2 \longrightarrow y=a^x+2$.
Use $(1, 5)$:
$y=a^x+2\\
5=a^1+2\\
5=a+2\\
5-2=a\\
3=a$
Therefore, the equation is $y=3^x+2$.
