Explain logistic growth.

(N/A) In nature, no population has unlimited resources to permit exponential growth. This leads to competition between individuals for limited resources. Eventually, the 'fittest' individual will survive and reproduce. Many governments have realized this and introduced various restraints to limit human population growth.
In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible. Let us call this limit as nature's carrying capacity $(K)$ for that species in that habitat.
A population growing in a habitat with limited resources shows initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity. A plot of $N$ in relation to time $(t)$ results in a sigmoid curve. This type of population growth is called Verhulst-Pearl Logistic Growth and is described by the following equation:
$dN/dt = rN \left( \frac{K - N}{K} \right)$
Where:
$N = \text{Population density at time } t$
$r = \text{Intrinsic rate of natural increase}$
$K = \text{Carrying capacity}$
Since resources for growth for most animal populations are finite and become limiting sooner or later, the logistic growth model is considered a more realistic model.