The functions $f$, $g$, and $h$ are defined by the given equations, where $x\ge 0$. For which of the following functions does a finite maximum value exist for $x\ge 0$?

I. $f(x)=100(1.01{)}^x$
II. $g(x)=50(0.95{)}^x$
III. $h(x)=75$