Logistic function
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}} where L {\displaystyle L} is the carrying capacity, the supremum of the values of the function; k {\displaystyle k} is the logistic growth rate, the steepness of the curve; and x 0 {\displaystyle x_{0}} is the x {\displaystyle x} value of the function's midpoint. The logistic function has domain the real numbers, the limit as x → − ∞ {\displaystyle x\to -\infty } is 0, and the limit as x → + ∞ {\displaystyle x\to +\infty } is L {\displaystyle L} .