# How does logistic growth occur?

##### 1 Answer

Logistic growth of population occurs when the rate of its growth is proportional to the product of the population and the difference between the population and its carrying capacity

with initial population

As you can see above, the population grows faster as the population gets larger; however, as the population gets closer to its carrying capacity

by separating variables and integrating,

by Partial Fraction Decomposition,

by multiplying by

Since

So, the equation becomes

by solving for

I hope that this was helpful.