## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$y=3^x+2$
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 $y=3^x+2$