WOLFRAM|DEMONSTRATIONS PROJECT

Logistic Model for Population Growth

​
P
0
100
r
0.08
K
1000
t
0
0
dP
dt
= r P(1-
P
K
​
P(t) =
K
A
-r t
e
+ 1
, A =
K-
P
0
P
0
Play the animation for consistent time steps.
exact
P
​
This Demonstration illustrates logistic population growth with graphs and a visual representation of the population. As time progresses, note the increase in the number of dots and how the rate of change increases but later decreases. Play the animation for
t
to see the behavior most clearly with discrete time steps. Compare this to exponential growth, presented in an analogous way in a companion Demonstration.