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 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:

\(\frac{dN}{dt}\) = rN \(\Big(\frac{K -N}{K}\Big)\)

\(\frac{dN}{dt}\) = rN \(\Big(1 -\frac{N}{K}\Big)\)

\(\Big(1 -\frac{N}{K}\Big)\) Environmental resistance