Logistic
Growth
A model for a quantity that increases
quickly at first and then more slowly as the quantity approaches
an upper
limit. This model is used for such phenomena
as the increasing use of a new
technology, spread
of
a disease,
or saturation
of
a
market
(sales).
The equation for the logistic model is .
Here, t is time, N stands for the amount
at time t, N_{0} is
the initial amount (at time 0), K is the maximum amount
that can be sustained, and r is the rate of growth
when N is very small compared to K.
Note: The logistic growth model can be obtained by solving the
differential equation
See
also
Exponential
growth, exponential decay
