Function with point of resistance

[rhenretta]

My maths is failing me. Take f(x), where f(x) wants to equalize at a value of 3,000,000. If it goes above, there is exponential resistance bringing it down, and as it goes below there is exponential growth driving it up. What would f(x) look like?

This is driving me nuts!

 

[JonF]

How you state this problem it doesn't make much sense. From what I understand you want to have a function that will change over x but you also want it to have an tendency towards 3,000,000 over some other variable like time?

If you let g(x) be your function:

if g(x) <= 3,000,000 then f(t,x) = g(x) + t/(t+1)|3,000,000 – g(x)|
if g(x) > 3,000,000 then f(t,x) = g(x) - t/(t+1)|3,000,000 – g(x)|