Logistic growth functions

Combines uninhibited growth, at first, then tapers off to a limiting value.
Growth is proportional to both the existing population and the amount of available resources.
S, Sigmoid shape curve.
Two different horizontal asymptotes.

L is the limiting population, carrying capacity, maximum, saturation.
C is a measure of available resources (e.g. food, space)
t is time, k is growth rate.

Limiting, carrying capacity (L):
Available resources (C):
k:

Evaluate N(t) for t:     OR     If N(t)= what is the time t?

N0: initial population.    = L/(C+1)
C=(L-N0)/N0

x0: x-value of the inflection point = ln C / k
y-value of the inflection point = L/2
The inflection point is the point of maximum increase. The curve is symmetric about this point.

           

Slow, almost constant, linear then exponential that becomes linear, then slow. almost constant linear again.
Zoom out: step function.
Phase transition: melt/freeze, boil/liquify.

Exercises