The function $f$ is defined by $f(x)=3(2^x+2^c)$, where $c$ is a positive integer constant. The functions $g$ and $h$ are equivalent to function $f$, where $k$ and $m$ are constants. Which of the following equations displays the $y$-coordinate of the $y$-intercept of the graph of $y=f(x)$ in the $xy$-plane as a constant or coefficient?

I. $g(x)=3(2^x+k)$
II. $h(x)=3(2^x)+m$