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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

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    "You need to clarify your question, it doesn't make much sense" - even a crude sketch of the curve you'd like to see would be awfully nice...2011-07-16

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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.

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Sounds like you want the Logistic function. The values are between 0 and 1, though the growth is centered around $0$ and it has an exponential in it. You can shift it horizontally by adding a constant to $x$ and change the steepness by changing $e^{-x}$ to $e^{-ax}$ for your choice of $a$. Does that work?

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    yeah.. similar but not quite there. this looks to be an s-curve, I'm looking for more of what was in the graph I linked above.2011-07-16