The problem describes a graph representing the growth of a fly population in a jar. The questions ask (a) which part of the graph (A, B, C, or D) indicates the carrying capacity of the jar, (b) how to arrive at the answer for (a), and (c) what would happen to the population graph if the food and water in the jar were not refilled.

Applied MathematicsPopulation GrowthCarrying CapacityGraph AnalysisModeling
2025/4/15

1. Problem Description

The problem describes a graph representing the growth of a fly population in a jar. The questions ask (a) which part of the graph (A, B, C, or D) indicates the carrying capacity of the jar, (b) how to arrive at the answer for (a), and (c) what would happen to the population graph if the food and water in the jar were not refilled.

2. Solution Steps

a. Carrying capacity refers to the maximum number of individuals an environment can support. On a population growth graph, the carrying capacity is represented by the plateau where the population growth levels off. In the given graph, section C represents the part of the graph where the fly population levels off. Therefore, the answer is C.
b. The carrying capacity represents the maximum sustainable population size that the environment can support given the available resources. In the graph, after section B, the rate of population growth slows down until it reaches a plateau in section C. This indicates that the population has reached the limit of what the jar can support in terms of resources such as food, water, and space. Therefore, I arrived at the answer by looking for the part of the graph where the population stopped growing.
c. If the food and water in the jar were not refilled, the fly population would eventually decrease. As the resources are depleted, the flies will begin to die off due to starvation and lack of water. The graph would show a decline after point C. The population would likely decline until it reaches a new equilibrium at a lower population level (if any resources are leftover) or zero (if all resources are completely depleted).

3. Final Answer

a. C
b. The carrying capacity is where the population stops growing and the graph plateaus, which is indicated by C.
c. If food and water are not refilled, the fly population would decrease over time, leading to a decline in the graph after point C.

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