This page invites exploration of "S-Shaped" or "Sigmoid" Curves. This family of curves have the mathematical formula:
y = max · x n / (k n + x n)
The 'max' parameter determines the maximum value of the curve. 'k' is called the "half-maximum" of the curve and has the following meaning: when x = k, y = 1/2 * max (i.e., y will be at half of its maximum value when x = k). 'n' controls how steeply the curve rises.
This page also allows investigation of the "Reverse Sigmoid" family of curves, given by the formula:
y = max · k n / (k n + x n)
where the parameters have the same meanings as with the regular sigmoid curve.
|Maximum Value (max)|