With regard to its rate of growth, a population that is growing logistically a. grows fastest when density is lowest. b. has a high intrinsic rate of increase. c. grows fastest at an intermediate population density. d. grows fastest as it approaches carrying capacity.

Verified step by step guidance

1. Understand the concept of logistic growth: Logistic growth describes how a population grows in an environment where resources are limited. It starts slow, speeds up, and then slows down as the population reaches the carrying capacity of the environment.
2. Identify the carrying capacity: The carrying capacity (K) is the maximum population size that the environment can sustain indefinitely. It plays a crucial role in logistic growth.
3. Analyze the growth rate at different densities: In logistic growth, the growth rate changes depending on the population density. It is not constant like in exponential growth.
4. Determine the point of fastest growth: The fastest growth in a logistic model occurs not when the population is at its lowest or highest, but at an intermediate level. This is because, at very low densities, there are too few individuals to maximize growth, and at high densities, resource limitations slow down growth.
5. Apply the concept to the options: With the understanding of logistic growth, evaluate which option correctly identifies when a population growing logistically grows fastest.

Key Concepts

Logistic Growth Model

The logistic growth model describes how a population grows in an environment with limited resources. Initially, the population grows exponentially, but as it approaches the carrying capacity of the environment, the growth rate slows down. This model is characterized by an S-shaped curve, where growth is rapid at first, slows as resources become scarce, and eventually stabilizes.

Carrying Capacity

Carrying capacity refers to the maximum number of individuals that an environment can sustainably support. It is determined by factors such as food availability, habitat space, and competition. As a population nears its carrying capacity, the growth rate decreases, leading to a balance between birth and death rates, which is crucial for understanding logistic growth.

Population Density

Population density is the number of individuals per unit area or volume in a given habitat. It plays a significant role in population dynamics, influencing competition for resources, reproduction rates, and mortality. In logistic growth, the growth rate is highest at intermediate population densities, where resources are still sufficient but competition is not yet limiting.