An exponential function between zero and one Alrighty, math noob here, so be nice :P. We're building an app and need an exponential function that exists between zero and one, and, depending on the importance we give it, will fluctuate between rising near the beginning or end of the graph. Lemme know if you have any ideas or need clarification :P

Maybe you mean power law rather than exponential. In that case @fedja's suggestion is great: $x^a$. $a<1$ for low importance and $a>1$ for high importance.