I tried the most basic y = 100*constant^(1/x) assuming that 1/x = 0 when x is infinity, but it doesn't seem to work.
This gives me a function that starts with a higher value of y and goes down till it reaches 100 at the value of infinity. But I want a rising value of y that reaches 100 only at infinity, and remains below 100 the rest of the time.
How about $f(x) = 100 + e^{-x}$? It has a limit of $100$ as $x\to\infty$ (by the way, it is better to speak of limits as $x$ approaches infinity, rather than being equal to it.