Function with output that initially increases input, but levels off and never surpasses a given value?

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I'm trying to find a function f(x) that will fit the following general pattern. Please note these aren't exact results but very rough approximations:

f(0) = 0; f(5) = 29; f(25) = 59; f(50) = 68; f(100) = 69;

So the output should be much higher than x while x is small, but it should level off after a while, never surpassing 70. I tried logarithms, but all the outputs I got were smaller than x. And adding a multiplier makes it grow past 70.

Any help would be appreciated!