A Malthusian growth model is a model of population growth in which the per-capita growth rate is constant. The continuous model satisfies
 |
(1)
|
where 
is the Malthusian parameter. For the initial
condition 
,
its solution is
 |
(2)
|
For 
,
the population doubles after 
.
The corresponding discrete-time model with fixed interval 
is
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
.
Because the growth rate does not decrease as 
increases, the model has no carrying
capacity. The logistic equation modifies
the growth rate to account for a finite carrying
capacity.
The model is named for the population theory of Malthus (1798).
