Three years of calculus in college have served me nothing, apparently, since I can't for the life of me remember even the basics. I'm working on a small software project where I have a table with say 20 cells, and I want the cells' opacity to go down as the index goes up.
Currently, I'm doing it linearly with $\textrm{opacity} = 1 - (\textrm{index}/20)$, or $y = 1-x$. The curve I'm going for is something where at the beginning I have a high value for the opacity, 1, but then it starts dropping like a roller-coaster, non-linearly. The best I can describe it is it looks like half of a 'C' draw on the positive xy axis.
The closest I got was $y = e^x$, but that plot goes up. Can anyone tell me the name of what I'm looking for?
Edit: Ok it turns out what I'm looking for is a hyperbola, $y = 1/x$. However, since this is a opacity value, the range needs to be from $0$ to $1$, while the domain is also $0$ to $1$. But I'm getting some large values for small inputs.