Function $f$ is defined by $f(x)=-a^x+b$, where $a$ and $b$ are constants. In the $xy$-plane, the graph of $y=3f(x)+2$ has a y-intercept at $(0,\frac{23}{2})$. The product of $a$ and $b$ is $\frac{15}{2}$. What is the value of $a$?