Question

\[\frac{{dN}}{{dt}} = rN(\frac{{K - N}}{K})\]
A - Population density at time t
B - Intrinsic rate of natural increase
C - Carrying capacity
Identify A, B and C from the given equation
A. ABC- NKr
B. ABC- NrK
C. ABC- KNr
D. ABC- KrN

Answer 1

Hint:
Before we proceed into the problem, it is important to know the definition of exponential population growth.
It is characterized as exponential growth when the population grows at a consistent rate across time and is never constrained by a lack of food or disease. The rate of change in population size is denoted by \[\frac{{dN}}{{dt}}\] Biotic potential is denoted by r and the population size is N. This formula for exponential growth is \[\frac{{dN}}{{dt}} = rN\left( {K - \frac{N}{K}} \right)\]

Complete step by step answer:
The number of people in a population (N) over time is used to calculate the population growth rate (t). Population growth rate’s symbol is (\[\frac{{dN}}{{dt}}\]). The change is denoted by r. K is the carrying capacity, and the maximum per capita growth rate is denoted by r.
Per capita refers to a person, and the per capita growth rate takes into account both the birth and death rates within a population. The logistic growth equation makes the assumption that K and r in a population do not alter over time.
When responses are limited with reference to the population growth rate, the plot is logistic. Pearl Verhulst The equation \[\frac{{dN}}{{dt}} = rN\left( {K - \frac{N}{K}} \right)\] represents the growth of a logarithmic function.
The Malthusian parameter, or r, denotes the maximum rate of population expansion.
The population's carrying capacity is K.
The total amount of people in a population is N.
Therefore, A represents N, B represents r, C represents K

Option ‘B’ is correct

Note:
In nature, no species of life have the capacity to develop exponentially indefinitely. The most adaptable organism will ultimately survive and reproduce. In nature, a specific habitat has the capacity to support a maximum number, after which no additional expansion is feasible. The carrying capacity of nature (K) for that species in that habitat is the upper limit. The rate of growth \[\frac{{dN}}{{dt}}\] decreases as the value of N rises.