A population growing in a habitat with limited resources show 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 population density $(N)$ in relation to time $(t)$ results in a sigmoid curve. Here, $r$ is intrinsic rate of natural increase and $\mathrm{K}$ is carrying capacity of the environment. This type of population growth is called Verhulst-Pearl Logistic Growth and is described by the

$\Rightarrow \quad \frac{d N}{d t}=r N\left(\frac{K-N}{K}\right) \quad \frac{d N}{d t}=r N\left(1-\frac{N}{K}\right)$

$\left(1-\frac{N}{K}\right)$ Environmental resistance.