What form would the formula describing this behaviour have?

Question

exponential(?) behaviour of my parameter as a function of temperature.

I have a simple question relating to the above figure. I want to fit (leastsquare) a line trough this data using a natural exponential. What form would such a formula have? I tried $f(x) = 1- Ae^{x/\tau}$ which gives a bit akward results. Is this the correct way to go and should I maybe focus on optimization of the initial guesses? Are there any parameter I can add to the forumula to improve the fit? Any ideas? Thanks a lot!

Answer 1

Let's call the parameter $p$ and the temperature $T$

I think the curve looks easier to fit once you choose on the $y$ axis, $(1-p)$, and on the x-axis $T-T_0$. Then the curve can be an exponential, or even a polynomial (like a quadratic).

Can you try

1. $1-p = c+a\exp(b(T-T_0)) \equiv p=c'-a\exp(b(T-T_0))$
2. $1-p = a_0+a_1(T-T_0)+a_2(T-T_0)^2$

This is heuristic based on the shape of the curves, and one can't say more without looking at the data.