Question

Which of the following equation is correct about Verhulst-Pearl Logistic Growth?

• A. \( \frac{dN}{dt} = (h - d) \frac{K - N}{K} \)
• B. \( \frac{dN}{dt} = rN \frac{N - K}{K} \)
• C. \( \frac{dN}{dt} = rN \frac{K - N}{K} \)
• D. \( \frac{dN}{dt} = (h - d) \frac{N - K}{K} \)

Hint:

The Verhulst-Pearl Logistic Growth equation describes the growth of a population in a limited environment. It accounts for the carrying capacity (K), which is the maximum population size that the environment can support. The equation is given as:

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

Where:

\(\frac{dN}{dt}\) is the rate of change of the population size,

\(N\) is the current population size,

\(K\) is the carrying capacity (maximum population size the environment can support),

\(r\) is the intrinsic growth rate (rate of reproduction).

This equation shows that as the population NNN approaches the carrying capacity KKK, the growth rate slows down, reflecting the limitations of resources.

Answer 1

The Correct Option is C

The Verhulst-Pearl Logistic Growth model is represented by the equation: 

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

Where:

• \( \frac{dN}{dt} \) 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.

This equation describes how the growth rate is proportional to both the size of the population and the available resources, considering the environmental limitations (carrying capacity). As the population size \( N \) approaches the carrying capacity \( K \), the growth rate slows down, leading to a sigmoid or S-shaped curve.

Therefore, the correct equation from the given options for Verhulst-Pearl Logistic Growth is: \( \frac{dN}{dt} = rN \frac{K - N}{K} \)