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

enter image description here

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!

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  • $\begingroup$ Did you try a simple $y(x) = a\,x^{b}$ ? It seems that it might work with $0<b<1$. $\endgroup$ Aug 25, 2023 at 17:01
  • $\begingroup$ What about $(1-e^{ax})b$ for some $a,b\in\mathbb{R}$? $\endgroup$
    – QC_QAOA
    Aug 25, 2023 at 17:02
  • $\begingroup$ I tried $y = ax^b$ but. couldn't get a decent slope. I will try $b(1 - e^{ax})$ $\endgroup$ Aug 25, 2023 at 18:47

1 Answer 1

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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]

enter image description here

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  • $\begingroup$ Amazing! Adding the sine helped me too! $\endgroup$ Aug 26, 2023 at 23:04

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