Function $f$ is defined by $f(x)=-a^x+b$, where $a$ and $b$ are constants. In the $xy$-plane, the graph of $y=f(x)-15$ has a $y$-intercept at $(0,-\frac{99}{7})$. The product of $a$ and $b$ is $\frac{65}{7}$. What is the value of $a$?