Derive Exponential Function From Limited Information

I've been working on a ss that requires me to create a function to determine a value from a exponential curve where the area of the curve is variable . The terminal points, 0,0 and 100,100 remain constant and the curve is symmetrical at the 45degree angle. How can I derive a function knowing only these things.

Here is an image to crudely illustrate what i mean [url]

The area can be 10, 20, 35% it doesn't matter, I need a way to determine the function from just the area!