Question

According to the logistic growth equation\(\frac{{dN}}{{dt}} = rN\frac{{(K - N)}}{K}\)

(A) the number of individuals added per unit time is greatest when Nis close to zero.

(B) the per capita population growth rate increases as Napproaches K.

(C) population growth is zero when Nequals K.

(D) the population grows exponentially when Kis small

Short answer

1. The statement “the number of individuals added per unit time is greatest when Nis close to zero” is false.
2. The statement “the per capita population growth rate increases as Napproaches K” is false.
3. The statement “population growth is zero when Nequals K” is true.
4. The statement “the population grows exponentially when Kis small” is false.

Step-by-step solution

Population ecology

The subdivision of ecology that focuses on species population and the associated change in them living in the same area including the environment, population size and distribution is called population ecology.

Explanation of option ‘(A)’

Logistic growth refers to a model that shows the growth rate of the population and its change as an exponential function.

Thus, the rate of the exponential increase of population slows down when N is close to zero.

Therefore, the given statement is false.

Explanation of option ‘(B)’

The growth rate in the logistic model shows the change in population rate over time based on the availability of resources like food space.

Thus, when N approaches K, the growth rate decreases.

Therefore, the given statement is false.

Explanation of option ‘(C)’

The birth rate, death rate, and migration are considered as three distinct elements affecting the population growth rate in the logistic model.

Thus, N (population density) is approaching K (carrying capacity); population growth does not grow exponentially and decreases with time until it becomes zero.

Therefore, the given statement is true.

Explanation of option ‘(D)’

The logistic growth curve indicates the exponential function of population growth with limited environmental resources.

Thus, when K (carrying capacity) is small, there will be no exponential growth of population.

Therefore, the given statement is false.