# Exponential equation with top and bottom limits?

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.

• Welcome to stackexchange. Please edit the question to clarify. Do you mean "exponential" literally, or just something that grows faster as the input gets closer to $100\%$? Your picture shows $100\%$ at a finite value. If you really want that only at infinity the curve will have to be levelling off. So will a fixed large finite upper limit do? Once you make the question clear we should be able to provide a curve where you can easily adjust the top and bottom limits and how fast the steepness increases. – Ethan Bolker Apr 12 at 22:50
• Hey and thank you, I'm sorry if my question was vague I'm not too familiar with the mathematical terms that are involved however I'm just looking for the equation for the line that I drew in the picture or something close to it. – Echo Apr 13 at 15:18