The function $f$ is defined by $f(x)=a^x+b$, where $a$ and $b$ are constants and $a>1$. In the xy-plane, the graph of $y=f(x)$ has a y-intercept at $(0,3)$ and passes through the point $(1,7)$. What is the equation of the horizontal asymptote of the graph of $y=f(x)$?