I dont know the exact equation. If you are using this on flow control charecteristic you can use exponential type of equation but not exactly Y=e^X. You can use y=a+b*(e^(x^n)-1) where you can find the values of 'a' and 'b' depending upon your boundary condition/initial conditions i.e based on the type of parameters used too. 'n' gives the smoothness of curve for example square or cubic.

I am not the mathematician but I like to apply mathematics.

Parbatya