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 defined by the equation:

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

Key variables are:

• \( \frac{dN}{dt} \): Population size change rate over time.
• \( r \): Population's intrinsic growth rate.
• \( N \): Current population size.
• \( K \): Environmental carrying capacity.

This formula illustrates that population growth rate is contingent on both population size and resource availability, constrained by the carrying capacity. As population size \( N \) nears carrying capacity \( K \), growth decelerates, resulting in a sigmoid or S-shaped trajectory.

Consequently, the accurate representation of the Verhulst-Pearl Logistic Growth equation among the options is: \( \frac{dN}{dt} = rN \frac{K - N}{K} \)