Question

population r has 10,000 members and is growing logistically by 5% (0.05) per year. if the population reaches its carrying capacity after the third year, what size will the population likely be fluctuating around after the fifth year?
10,000–11,000 members
11,000–12,000 members
13,000–15,000 members
15,000–20,000 members
which graph most closely resembles the growth of population r?

Explanation:

Logistic growth is characterized by an S - shaped curve. In logistic growth, the population grows until it reaches the carrying capacity. Once the carrying capacity is reached (after the third year in this case), the population will fluctuate around the carrying capacity.

• First - year growth: \(10000\times(1 + 0.05)=10500\)
• Second - year growth: \(10500\times(1 + 0.05)=11025\)
• Third - year growth: \(11025\times(1 + 0.05)\approx11576\)

Since the population reaches its carrying capacity after the third year, it will fluctuate around that value. The value \(11576\) falls in the \(11000 - 12000\) range.
For the graph, the S - shaped curve (where the population first has a period of growth and then levels off) is the characteristic of logistic growth.

Answer:

For the population size: \(11,000 - 12,000\) members.
For the graph: The graph with the S - shaped curve (the second graph in the set of four graphs, which shows a population starting from a relatively low value, increasing rapidly and then leveling off).