Q: What am I trying to accomplish?
A: I am trying to derive a mathematical function for an inverse signoid line that starts out at the max value and over time declines to a min value that I define.
$ CPC is plotted on the Y axis, Total cost is plotted on the X axis. I am trying to determine what the $ CPC (between $0.00 & $10 for example) should be given a certain level of total cost (between $0.00 & $100 for example)
Here's a picture the function I am trying to derive.
I basically want the formula to start out at the Max CPC (Let's say $10) and as cost increases, to decrease logarithmically but not below a MIN CPC value (Let's say $0.50). At the MIN CPC value, I want it to be a horizontal asymptote.
Is there a function that will let me input the Max CPC and MIN CPC to be the Ceiling and Floor and then essentially decay based on the level of Total Cost?