The problem presents a graph showing the changes in the size of a trout (fish) population over time. It asks: a. What does the dashed line represent? b. What is the approximate number that represents the carrying capacity of trout in this area? c. How did you arrive at your answer for 3b.? d. Trout eat insects. What would happen to the carrying capacity of trout if people sprayed chemicals to kill bugs in this area?

1. Problem Description

The problem presents a graph showing the changes in the size of a trout (fish) population over time. It asks:

a. What does the dashed line represent?

b. What is the approximate number that represents the carrying capacity of trout in this area?

c. How did you arrive at your answer for 3b.?

d. Trout eat insects. What would happen to the carrying capacity of trout if people sprayed chemicals to kill bugs in this area?

2. Solution Steps

a. The dashed line on the graph represents a horizontal asymptote for the population growth. This indicates a limit on the population size. The dashed line represents the carrying capacity.

b. Looking at the graph, the dashed line is approximately at the $400$ mark on the population axis.

c. I arrived at the answer for 3b by visually inspecting the graph. The population size oscillates around the dashed line after a period of initial growth, suggesting that the dashed line represents the carrying capacity. The population stabilizes around $400$, so $400$ is the carrying capacity.

d. If people sprayed chemicals to kill bugs in the area, and trout eat insects, the food source for the trout would be reduced. This would lead to a decrease in the carrying capacity of trout in the area, as the environment would be able to support fewer trout due to the limited food availability.

3. Final Answer

a. The dashed line represents the carrying capacity.

b. The approximate number that represents the carrying capacity of trout in this area is $400$.

c. I arrived at the answer for 3b by observing the graph and noting the population stabilized around $400$.

d. The carrying capacity of trout would decrease.