Question: 180. Which one of the following equations represents the Verhulst-Pearl Logistic Growth of population?
(1) \frac{d N}{d t}=r\left(\frac{K-N}{K}\right)
(2) \frac{d N}{d t}=r N\left(\frac{K-N}{K}\right)
(3) \frac{d N}{d t}=r N\left(\frac{N-K}{N}\right)
(4) \frac{d N}{d t}=N\left(\frac{r-K}{K}\right)
Answer: Option (2)
Explanation:
The Verhulst-Pearl logistic growth model describes population growth under limited resources.
In this model, population growth rate initially increases but gradually decreases as the population size approaches the carrying capacity K of the environment.
The general form of the logistic growth equation is given by:
\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)This can be rewritten as:
\frac{dN}{dt}=rN\left(\frac{K-N}{K}\right)Here, N is the population size, r is the intrinsic rate of natural increase, and K is the carrying capacity.
This equation shows that as N approaches K, the growth rate decreases and eventually becomes zero.
Therefore, option (2) correctly represents the Verhulst-Pearl logistic growth of population.