Final answer:
In logistic growth, the per-capita population growth rate initially increases, then declines as the population density approaches the carrying capacity (K), forming an S-shaped curve. It reaches a peak before K and does not increase with increasing density past a certain threshold.
Step-by-step explanation:
Logistic Population Growth
For a population growing in a logistic fashion, the per-capita population growth rate displays a unique pattern. During logistic growth, a population initially grows exponentially when there are abundant resources. As the population approaches the carrying capacity (K) of the environment, the growth rate slows and eventually levels off. Logistic growth is represented by an S-shaped curve. The per-capita growth rate therefore increases at first due to the exponential growth, but as the population density increases, it reaches a point where growth slows down due to limited resources and other density-dependent factors.
Answering the student's choices:
- b. The per-capita population growth rate increases, then declines in a hump-shape curve as resources become limited.
- c. The population reaches its maximum growth rate at an intermediate population size, not necessarily at K; after this point, growth rate declines as it approaches K.
- The per-capita growth rate does not increase with increasing density beyond a certain point, contrary to what would be expected in exponential growth.