Explanation:
The Verhulst Pearl logistic Growth (VPGL) can be described by the equation:
dN/dt = rN (K–N/K)
where:
- dN/dt represents the rate of change of the population size over time
- r is the intrinsic growth rate of the population
- N is the current population size
- K is the carrying capacity of the environment, i.e., the maximum population size that the environment can sustain
Let's break down the equation and understand its components:
1. dN/dt:
- This represents the rate of change of the population size over time.
- It indicates how fast the population is growing or declining at any given time.
2. rN:
- This term represents the intrinsic growth rate of the population multiplied by the current population size (N).
- It indicates the potential for population growth in the absence of any limiting factors.
3. (K–N/K):
- This term represents the fraction of the carrying capacity (K) that is available for population growth.
- It is calculated by subtracting the current population size (N) from the carrying capacity (K) and dividing it by the carrying capacity (K).
4. rN (K–N/K):
- This term represents the product of the intrinsic growth rate (rN) and the fraction of carrying capacity available for population growth ((K–N/K)).
- It combines the potential for population growth (rN) with the availability of resources (K–N/K).
Overall, the equation describes the population growth rate as a function of the current population size, the intrinsic growth rate, and the carrying capacity. It takes into account the limitation of resources as the population approaches the carrying capacity, leading to a decrease in the growth rate.
Therefore, the correct answer is B: dN/dt = rN (K–N/K).

The Verhulst pearl logistic growth (VPLG) model is given by dN/dt = rN(1-N/K) where N is the number (density) of indviduals at time t , K is the carrying capacity of the population, r is the intrinsic growth rate of the population....Thus, option B is right ans..