Find equation to fit data with plateau

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I have a dataset with X and Y values. I would like to fit the data which plateaus at a certain value Y (want to extract the Y where it plateaus).

The data includes (0 0) and for increasing x (no limit) the Y values do not increase beyond a certain Y value.

Plateau for distance vs square root of time

Plateau for distance vs time

What would be the (most suitable) fitting function?

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You can fit $$ y = M(1- e^{-ax}) $$ where $M$ is the maximum at which the plateau ends up and $a$ governs how fast it gets there.

You can probably get Excel to find the best values of $M$ and $a$, or just play until the graph looks right.