Let $s(x)=b(4^x+4^a)$ where $b$ and $a$ are integers such that $0<b<a$. Define $t(x)=b(4^x+p)$ and $r(x)=b(4^x)+q$, where $p$ and $q$ are constants. Determine which, if any, of the functions expresses the y-coordinate of the y-intercept of the graph of $y=s(x)$ in the $xy$-plane as a constant or coefficient.