Exponential equation with top and bottom limits?

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So I'm coding a interactive sliding bar that changes based on the value that is given. Currently the interaction between the value given and the bar is static and I would like to make it flow with the input that it is given.

I want to take a number from 0-infinity(more likely around 50,000 - 100,000) and with this number receive and output of a percentage with in account of the upper and lower threshold.

I Illustrated this for the problem. (I've never learned calculus so I'm having problems)

Example Picture

I'm assuming there is some easy way to do this setting top and bottom limits to a exponential curve.

Another plus if possible I'd like to be able to manipulate the upper and lower threshold with just an integer. I'm not sure it that is possible.