Sigmoid function - Wikipedia, the free encyclopedia
In general, to get the curve to take only positive x axis values you will have to take the natural log of the argument x. And to get it to face the direction you want (like in your graph) you will have to multiply the function by -1 and add 1. Here are three functions I just tried out on my grapher which seem to match what you're asking for:
Below, the constant "a" is just "Max CPC" minus "Min CPC". You will have to interpret 0 as the Min CPC.
Using the error function:
Manipulating the log-logistic function:
(you can also try removing the square from the x)
And my personal favorite:
They each "decay" according to different principles. I like the last one the best because 1/x is the elasticity of the function with respect to x, which to my mind models the rate of decay to total cost relation in a clear way.