Question

In the formula $G=rN\left(\dfrac{K-N}{N}\right)$ , the factor $rN$ tends to cause the population to-
(A) remain stable at the carrying capacity
(B) grow at a slower rate than the $\left(\dfrac{K-N}{N}\right)$ factor
(C) grow increasingly rapidly
(D) decrease in size

Answer 1

Hint: In this question, such equations represent logistic growth rate of a population. Here, each of the letter represent one or the other thing, for example $K$, $rN$ everything has its own different meaning, and all these meanings are related to population growth models.

Complete Step-by-Step Answer: An unchanging age structure and an exponential growth rate r are characteristics of a stable population; vital rates govern both the structure and the growth rate (mortality, fertility). An individual organism lacks some characteristics, whereas a population does. A population's birth and death rates are different from an individual's birth and death rates. These rates apply to per capita births and deaths within a population. Growth Models: Does the expansion of a population over time follow a definite, observable pattern? It is only reasonable for us to wonder whether other animal populations in nature act similarly or exhibit growth limitations given our concern over unchecked human population growth and the problems it has caused in our nation.

Logistic growth: In nature, no population of any species has access to enough resources to support exponential expansion. As a result, people compete with one another for scarce resources. The "fittest" individual will eventually prevail and procreate. This reality has also been acknowledged by many governments, who have responded by enacting a variety of restrictions designed to slow the rate of population growth. A specific habitat in nature has enough resources to support a maximum number, after which no additional growth is conceivable. Let's refer to this cap as the carrying capacity of nature $(K)$ for in that environment with that species.

In the equation given in the question: Where r is the intrinsic rate of natural increase and $N$ is the population density at time $t$, carrying capacity, $K$. $N$ represents the size of the population, and r is the difference between the birth and death rates. The population growth rate is therefore $rN$.

So, option (C) is correct.

Note: In logistic growth, a population's rate of per capita growth declines as it approaches the carrying capacity, a limit imposed by the environment's limited resources $(K)$. A $J$-shaped curve is produced by exponential growth, whereas an S-shaped curve is produced by logistic growth.