Rate of growth comparison: 1-20 xp to x^2,x,log(x)

[kb2005]

Was trying to figure out a fair way to price partial powerlevels in the 1-20 range, and my initial intuition was to base it off the amount of experience required for each level divided by the total xp needed to reach level 20. Turns out this more or less matches the growth for f(x) ~= 0.035x^2 (orange,) which I think unfairly weights the price distribution at the later levels. So, I tried a linear distribution which was better, but ultimately decided log(x) would be the most fair.

Anyway, for funsies / show and tell I decided to graph all that out so you can see how the actual xp rate of growth from 1 to 20 compares to other functions.