# Logistical Curve Tansformations

Mostly I am having a brain fart. Working on a game and wanted to use logistical curve for the experiance gain of skill levels. Idea is to create a system the reflects natural learning; early on you are too ignorant to learn quickly needing to learn the terms/basic concepts, from beyond that you learn pretty quickly until you reach a point requiring specialization which it slows and takes VERY SPECIFIC training and purpose.

I'm used to the very basic example of the curve f(x)=1/1+e^-k(x-xo)

Easy enough to shift the curve over to the midpoint I want. And I can alter the steepness of the actual curve. When I get into stretching out how it acts though I get bit lost. There are several versions of the equation. I'm not sure which would best fit. Which would allow the best for this.

I would like there to be a slow exponintal growth from values that give y=~0=20 y=~21-60 or 75 I would like it to progress faster, requiring less increase in x for it to go higher. At values y=75+ I would like it to require SIGNIFICANTLY higher values actually approaching but never reaching 100.

This will then translate to x=current experience points, and y=percent known in the skill

there are several versions of the equation. And I've never had a class that covers this. My knowledge is self taught. So i'm not sure how or why each is derived and what the long term effects/results could be at high experience values (obviously eventually Ill have a rounding error that gives out y=100)

Taking the time to try out each equation in the pretty poor graphing calculators online are tedious, and dont give the depth of knowledge I might end up needing (not to mention the time to get it set to values I really want) So just gentle push in the right direction to aid in efficiency would be appreciated.