Logistic Function

A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation:

${\displaystyle f(x)={\frac {L}{1+\mathrm {e} ^{-k(x-x_{0})}}}}$

where

• e = the natural logarithm base (also known as Euler's number),
• x₀ = the x-value of the sigmoid's midpoint,
• L = the curve's maximum value, and
• k = the steepness of the curve.^[1]

For values of x in the range of real numbers from −∞ to +∞, the S-curve shown on the right is obtained (with the graph of f approaching L as x approaches +∞ and approaching zero as x approaches −∞).
The function was named in 1844–1845 by Pierre François Verhulst, who studied it in relation to population growth.^[2] The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.
The logistic function finds applications in a range of fields, including artificial neural networks, biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, and statistics.

https://en.wikipedia.org/wiki/Logistic_function#Applications 

S Curves Everywhere