A population's carrying capacity a. may change as environmental conditions change. b. can be accurately calculated using the logistic growth model. c. increases as the per capita population growth rate decreases. d. can never be exceeded.

Verified step by step guidance

1. Step 1: Understand the concept of a population's carrying capacity. Carrying capacity refers to the maximum number of individuals of a particular species that an environment can support over a long period of time. It is determined by the availability of resources such as food, water, and space, as well as other environmental factors.
2. Step 2: Evaluate each option individually. Option a suggests that carrying capacity may change as environmental conditions change. This is true because changes in environmental conditions can affect the availability of resources, thereby affecting the carrying capacity.
3. Step 3: Option b suggests that carrying capacity can be accurately calculated using the logistic growth model. This is partially true. The logistic growth model can estimate carrying capacity, but it may not always be accurate because it assumes that all individuals have equal access to resources and that the environment is stable, which is not always the case.
4. Step 4: Option c suggests that carrying capacity increases as the per capita population growth rate decreases. This is not necessarily true. The carrying capacity is determined by the environment's resources, not the population growth rate.
5. Step 5: Option d suggests that carrying capacity can never be exceeded. This is not true. A population can temporarily exceed its carrying capacity, but this usually leads to a population crash because the environment cannot support the excess individuals.

Key Concepts

Carrying Capacity

Carrying capacity refers to the maximum number of individuals of a particular species that an environment can sustainably support. It is influenced by factors such as resource availability, habitat space, and environmental conditions. Changes in these factors can lead to fluctuations in carrying capacity over time.

Logistic Growth Model

The logistic growth model describes how populations grow in an environment with limited resources. Initially, populations grow exponentially, but as they approach the carrying capacity, growth slows and stabilizes. This model illustrates the relationship between population size and resource limitations, making it a useful tool for predicting population dynamics.

Per Capita Population Growth Rate

The per capita population growth rate is the average increase in population size per individual over a specific time period. It is a crucial factor in determining how quickly a population can grow. As this rate decreases, it often indicates that the population is nearing its carrying capacity, leading to a more stable population size.