Identify the equation representing logistic growth of a population.

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

The correct answer is Option (1)- \(\frac{dN}{dt} = rN\left(\frac{K - N}{K}\right)\)

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:

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

Where N = Population density at time t
r = Intrinsic rate of natural increase
K = 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 one.