Forgive my title. I want to model a number to act as a multiplier that is tied to a population source. Ideally the function(s) would have a value of 1 at 55,000, while increasing as the population increases or decreases, such that at a pop of 500 it would be close to 3, and at 5,000,000 it would also be 3, or somewhere in the positive single digits.
The purpose of this is for a simulation I'm cooking up in Excel to model a drug research trial using my own assumptions, that may not necessarily reflect reality. My assumption is that isolated places with small populations may be more susceptible to depression, while highly urbanized areas would also tend to be that way, while 55,000 could possibly be an ideal population. There are other variables I consider, but to keep it somewhat simple I'm not looking to include them at this point.
I've tried a couple things that haven't quite panned out, but came close in some regards:
This shows the table of results from the attempts. There were a few others not worth showing: Green areas are within reason; chart is of formula 2
