Question

Verhulst –Pearl logistic growth described by the equation $\dfrac{{dN}}{{dt}} = rN\dfrac{{[K - N]}}{N}$, where r and K represent.
A. r- intrinsic rate of natural decrease, K – carrying capacity
B. r-intrinsic rate of natural increase, K – carrying capacity
C. r-extrinsic rate of natural increase, K- productive capacity
D. r-extrinsic rate of natural decrease, K- carrying capacity

Answer 1

Various models for explaining the pattern of growth in a population have been given. Two of the most frequently used models are the logistic growth model and the exponential growth model. The exponential growth model explains about the doubling growth pattern in population example bacteria. The logistic growth model however is based on the growth with resistance from nature and other parameters.

Complete step-by-step solution:
Option A: This option is incorrect because r refers to the intrinsic rate of natural increase.
Thus, this option is not correct.
Option B: This option is correct because r refers to intrinsic rate of natural increase and K refers to carrying capacity. Intrinsic rate of natural increase (r) refers to total number of births minus the total number of deaths per generation of the population whereas carrying capacity (K) refers to the ability of an environment to support a limiting number of individuals, it is defined by the availability of space and nutrition in an environment.
Thus, this option is correct.
Option C: This option is not correct because r is not the extrinsic increase and K is also not the productive capacity.
Thus, this option is not correct.
Option D: This option is not correct because r refers to the intrinsic rate of natural increase.
Thus, this option is also not correct.
Option B is the correct answer.

Note: Exponential growth is not a very sustainable state because it relies on an unlimited number of resources (which usually don't exist in the real world). When there are fewer people and more resources, exponential growth may continue for a period of time. When the number of individuals increases enough, resources begin to run out, thereby slowing growth. Eventually, the growth rate tends to stabilize or stabilize and form an S-shaped curve. The maximum population size that a given environment can support is called the carrying capacity.