According to the logistic growth equation dNdt=rN(K−N)K a. the number of individuals added per unit time is greatest when N is close to zero. b. the per capita population growth rate increases as N approaches K. c. population growth is zero when N equals K. d. the population grows exponentially when K is small.

Key Concepts

Logistic Growth Model

The logistic growth model describes how a population grows in an environment with limited resources. It is characterized by an initial exponential growth phase, followed by a slowdown as the population approaches the carrying capacity (K) of the environment. The equation dN/dt = rN(K-N)/K illustrates how the growth rate (dN/dt) depends on the current population size (N) and the carrying capacity.

Carrying Capacity (K)

Carrying capacity (K) is the maximum population size that an environment can sustain indefinitely without being degraded. As a population approaches K, the growth rate decreases due to limited resources, leading to a stabilization of the population size. Understanding K is crucial for predicting population dynamics and managing ecological systems.

Population Growth Rate

The population growth rate refers to the change in population size over time, influenced by factors such as birth rates, death rates, immigration, and emigration. In the logistic growth model, the per capita growth rate decreases as the population size (N) approaches the carrying capacity (K), indicating that resources become more limited and competition increases, ultimately leading to zero growth when N equals K.