Many times the growth of a population is constrained. For
example the Edwards Plateau can sustain only a certain number of
deer. Otherwise they would eat all of the food available to them
and would then starve to death. Similarly, there is a limit to
the number of "Tickle Me Elmo" dolls that can be sold
by Walmart. While at first the growth in the number of deer or
the number of doll sales appears to be exponential there is a
limit to growth placed by the limited resources. This growth rate
is described by the relationship 
where M is
the maximum population that can be sustained by the region. The
solution to this differential equation (an equation that involves
a derivative) is given by 
. The table to the right and the graph
below are an example of logistic growth curve.
| t | y(t) |
| 0.00 | 2.27 |
| 1.00 | 3.54 |
| 2.00 | 5.34 |
| 3.00 | 7.74 |
| 4.00 | 10.62 |
| 5.00 | 13.73 |
| 6.00 | 16.69 |
| 7.00 | 19.20 |
| 8.00 | 21.13 |
| 9.00 | 22.50 |
| 10.00 | 23.42 |