Ok so I think this is pretty cool. I also think this is one of THE ways you should create core mechanics.
Simply - I'm creating a jump in a game, but this is so important to get right. A good jump is a little bit of positive feedback every time you hit the button. It can be addictive and genuinely fun. A bad jump makes you feel like you're fighting against the controls. In fact most people don't notice when a jump is good or bad, they just like one game and not the other and they don't know why. This stuff is important.
So this is how I'm doing it -
I'm using this easing function generator to create and tune the appropriate curve and then converting the function into C# and plugging it into my code. This is the initial result using a standard curve, it's not right yet but it already feels like it's on the way.
Next I need to gut that site's (very kindly freely available) code and create a solution that will give me more control over the curve and allow live editing