The function $f$ is defined by $f(x)=A\cdot B^x+C$, where $A$, $B$, and $C$ are constants and $B>0$. In the xy-plane, the graph of $y=f(x)$ has a y-intercept at $(0,10)$ and passes through the points $(1,15)$ and $(2,25)$. What is the value of $f(3)$?