Question

What is the formula for logistic growth, if $r$stand for the intrinsic rate of growth, $N$ for the number of organisms in a population, and $K$ for the carrying capacity?
A. $rN(N-K)/K$
B. $rN(N-r)/rK$
C. $rK(K-N)/rN$
D. $rK(r-N)/K$
E. $rN(K-N)/K$

Answer 1

Hint: As resources become scarce, population expansion decreases in logistic growth. In addition to it, logistic growth is inversely proportional to the availability of resources. Carrying capacity can be defined as the maximum population sustained in an environment where food, shelter, and other resources are available.

Complete answer: Depending on the availability of resources the population exhibits two types of growth. They are classified as exponential growth and logistic growth. In exponential growth resources are unlimited which results in a J-shaped curve. On the contrary, when resource availability is limited the population shows logistic growth. Here population expansion decreases as the resource’s availability decreases. It results in an S-shaped curve also called a sigmoid curve when the carrying capacity of the environment is reached. Equation of logistic growth can be given as $dN/dt=rN(K-N)/K$ where $r$ stands for intrinsic rate of growth, $N$ stands for the number of organisms in a population, and $K$ stands for the carrying capacity.
So, from the above options provided option E is the right answer as it defines the logistic growth of the population.

Note: The value of $r$ can be both positive and negative this indicates an increase in the population and decrease in the population respectively. It can also be zero meaning no change in the population. This condition is called zero population growth. Due to medical advances, lower mortality rates, and an increase in agricultural productivity have led to an increase in the human population. On the contrary in some countries, the population is decreasing because of low fertility rates, high death rates, and emigration.