Which function matches this shape?

Question

I'm trying to find a function that matches the following shape.

My first attempt was with a cosine function

$$ f(x) = a\cos(b x)$$

which yields the following result:

What modification of the cosine function could help to make it better fit the required shape? Any ideas or suggestions are appreciated.

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EDIT: the raw data is available in csv format here.

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EDIT 2:

Simple polynomial functions do not seem to yield better results.

Order 2:

Order 3:

Order 5:

For $f(x) = C-Ae^{bx}$ as suggested by @FranCruz I find

Answer 1

My first instinct looking at that data was 'parabola' (quadratic polynomial). It looks like a concave down parabola. I think you can get a good degree 2 polynomial fit for this data.