I am looking for a way to convert any number to a percentage in the following way:
1.00 is 50%
numbers below 1.00 approach 0% logarithmically
numbers above 1.00 approach 100% logarithmically.
x > 0. So y needs to approach 0 as x becomes infinitely small on the positive side.
I'm sure this is simple to do, but I can't recall how to do it.
try 1 / (1 + e^(1-x))
it's the logistic function shifted by 1 unit
If you want it to approach faster, you can change e to something higher
Edit:
to have f(0) = 0 you could use 1 - 2^(-x)