The following is what I am hoping to accomplish:
The main points here are:
- It curves
- It can't ever reach $1$
- Any number can be supplied for $X$
- The resulting $Y$ gets the most 'bang for its buck' earlier on the $X$
- $Y$ past a certain point (lets say around $1$ on the $X$) goes up really really slowly
I'm a game developer, and I need this so that the higher a supplied X goes, it never hits $1$ on the $Y$, but there is at least a little room for growth early on (between like $0.01$ and $0.5$ish on the X). Think of like 'run speed' of your character... there is a real limit on how fast a character should feasibly be able to run, but if someone were to level up their ability to run really high, there should be diminishing returns that total under the fastest the game should ever allow, but still allowing for growth (for instance, if $X$ is $10$, it should be extremely close to $1$ on the $Y$, but it still should be lower on the $Y$, than $20$ on the $X$).
Thanks in advance for all of your help! I don't have any better place to ask this, so your help is very very appreciated!