Ease numbers in a certain range I'm trying to find an easing function taking in values from `0` to `π/4` and outputting values in the same range, which starts really slow and exponentially accelerates toward full speed. Something like this: !enter image description here Thanks for your time!

If you want a vertical asymptote at $x=\frac{\pi}4$ you may try something like : $$f(x):=\frac{\pi}4\left(1-\sqrt{1-\left(\frac {4x}{\pi}\right)^4}\right)$$ !picture with vertical asymptot

Should you prefer an exponential grow near $\frac{\pi}4$ then you may try : $$\frac {\pi}4\left(\frac {4x}{\pi}\right)^4 e^{\frac {4x}{\pi}-1}$$ !exponential grow

(you may 'tune' these propositions by replacing the power $4$ with other values and so on...)