Manipulating the behavior of an exponential function (Math gurus needed!)

So, other thread didn't help much? http://arduino.cc/forum/index.php/topic,115296.0/topicseen.html
I'd suggest, before you try to program equation in C, you need clear representation of this equation in math with all coefficients defined, only after that you would be able to make a decision what "library" function is the best for task ( pow, exp, base 2, base 10, float vs integer etc).
The simple solution is Excell, or LibreOffice, where you play around with math, and see how it affects a chart. Only when you like what you see, you ready to transfer it in C.