I'm trying to change the steepness of an inverse exponential curve, whilst keeping (0,1) and (1,0) as fixed points, by changing the variables in the formula y = (a/(x+b))-b. Two examples of correct curves would be a=1, b=~0.618, and a=2, b=1. I need to know how to find b in terms of a, so that I can adjust the curve dynamically with a single input.
Could somebody please help me with this?
Thanks a lot!