What is the function behind this graph?

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enter image description here

Does anyone have an idea on what the function behind the graph might be? It seems to be similar to something like $a-(1/(1+e^(ln(x)-b))$ but less continuous in the end.

Note: the $x$-axis is Logarithmic scale.

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This is absolutely not an elementary function. If has at least four different regimes. Unless you have an idea of the underlying physical phenomena, you can fit lots of models to that, provided you introduce enough degrees of freedom.

You'd better whatch it with a bilogarihtmic scale.