Function form to fit a nonlinear trend

Question

I'm trying to guess a function that would fit the non-oscillating part of the following curve:

I tried something in the form of $y = 1 - e^{-ax}$ and $tan^{-1}(ax)$, but it didn't work since the trend becomes horizontal for extremely low values of $y$.

Are there any better suggestions to try?

Thank you!

Answer 1

Hint.

a = 0.05;
b = 1/2000;
r = 0.004;
y = a (1 - Exp[-b t]) + r Sin[10 2 Pi/2900 t]
Plot[y, {t, 0, 3000}, AspectRatio -> 0.8]