I'm not very familiar with math terminology so sorry if slope is the wrong word for a exponential function. I'm making a program, and in said program I currently have a value between $0$ and $1$, (lets call it $a$) and a time ($t$). The problem is that $a$ always = $t$, and that leads to it feeling really robotic and linear. What I want is to have a user defined "slope" and have that dictate how it moves. But I also need it to be so that when
$t = 1, a = 1$
and when
$t = 0, a = 0.$
But for the values in-between, it exponentially speeds up.
Best Answer
Choose a number $b>1$ and try $a=\frac{b^t-1}{b-1}$. You can try different values of $b$ to see what fit your requirements better.
Another option (although not exponential, but going increasingly faster) is to take $a=t^b$.