Looking for a systematically flattening function

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I kind of feel stupid asking this, but I can't figure it out.

What I'm looking for is a function that incrementally flattens out at specific points.

y = x/100 is fine for the first 10 y, but after that a single point of y will require 200 points.

Then at y = 20 the rate increases again to 300 x per y. At 30 it increases to 400, at 40 to 500, etc.

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Technically what I'm looking for is a step function that increments only when the threshold is reached, but I can take care of that afterwards using rounding.

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What sort of function would have behaviour like this?