The term (K−N)/K a. is the carrying capacity for a population. b. is greatest when K is very large. c. is zero when population size equals carrying capacity. d. increases in value as N approaches K.

Verified step by step guidance

1. Identify the terms in the expression (K−N)/K, where K represents the carrying capacity and N represents the current population size.
2. Understand that the expression (K−N) represents the difference between the carrying capacity and the current population size, indicating how much more the population can grow before reaching the carrying capacity.
3. Recognize that dividing (K−N) by K converts this difference into a proportion of the carrying capacity.
4. Analyze the expression when N equals K. If N is equal to K, then (K−N) becomes 0, making the entire expression (K−N)/K equal to 0.
5. Evaluate the behavior of the expression as N approaches K. As N gets closer to K, the value of (K−N) decreases, making the value of (K−N)/K decrease as well.

Key Concepts

Carrying Capacity (K)

Carrying capacity (K) refers to the maximum number of individuals of a particular species that an environment can sustainably support. It is determined by the availability of resources such as food, water, and habitat space. When a population reaches its carrying capacity, growth slows and stabilizes, as resources become limited.

Population Size (N)

Population size (N) is the total number of individuals of a species within a specific area at a given time. It fluctuates due to factors like birth rates, death rates, immigration, and emigration. Understanding the relationship between N and K is crucial for predicting population dynamics and ecological balance.

Logistic Growth Model

The logistic growth model describes how a population grows in an environment with limited resources. It is represented by the equation (K−N)/K, which indicates the growth rate decreases as N approaches K. This model illustrates that as resources become scarce, the growth rate slows, leading to stabilization at the carrying capacity.