Equation of Rapidly Increasing Line

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I think this is a straightforward problem, but it has been a long time since I've had to think like this.

I have approximately 50,000 [x, y] values collected as part of an experiment and I'm trying to come up with an equation that will return y for any given x. x values range from 1-100, but the vast majority occur early on (1-90 accounts for about 8% of the values in the data table). After that, there is an extremely sharp spike after 99. Example shown in the image below:

Increasing Line Image

What kind of equation am I trying to write here if I want to determine a y for a given x? I don't think this quite follows an exponential pattern. Thanks.

Requested Log Graph:

Log Graph