Editing Population growth (section)

===Logistic equation===

The growth of a population can often be modelled by the [[Population dynamics#Logistic population growth|logistic equation]]<ref>{{Cite book|title=Brief Applied Calculus|last1=Stewart|first1=James|last2=Clegg|first2=Daniel|publisher=Brooks/Cole Cengage Learning|year=2012}}</ref>

:<math>\frac{dP}{dt}=rP\left(1-\frac{P}{K}\right),</math>

where
* <math>P(t)</math> = the population after time t;
* <math>t</math> = time a population grows;
* <math>r</math> = the relative growth rate coefficient;
* <math>K</math> = the carrying capacity of the population; defined by ecologists as the maximum population size that a particular environment can sustain.<ref name=":0" />

As it is a separable differential equation, the population may be solved explicitly, producing a [[logistic function]]:

:<math>P(t)=\frac{K}{1+Ae^{-rt}}</math>,

where <math>A=\frac{K-P_0}{P_0}</math> and <math>P_0</math> is the initial population at time 0.