Question

$\frac{\mathrm{dN}}{\mathrm{dt}}=\mathrm{rN}\left(\frac{K-N}{K}\right)$ describes ________________.

• A. exponential growth model
• B. logistic growth model
• C. unrealistic growth model
• D. geometric growth model

Answer 1

The correct option is B logistic growth model

In a logistic growth model, a population in a habitat has limited resources. It initially shows slow growth (lag phase), followed by phases of acceleration (log phase) and then deceleration. It finally reaches the last phase (stationary phase) in which it attains carrying capacity i.e the maximum number of individuals of a population that can be sustained in a given habitat. After reaching carrying capacity, population growth slows down or stops altogether. This can be described by the following equation:

$\frac{\mathrm{dN}}{\mathrm{dt}}=\mathrm{rN}\left(\frac{K-N}{K}\right)$where ,
N represents the population density i.e the number of individuals in the population in particular time period t
r is the intrinsic rate of natural increase i.e the difference between birth rate and death rate in a population
K is the carrying capacity