Question

1. the population of mosquitoes rose significantly after a rainfall. afterward, the population slowly decreased until it reached a sustainable level. the population did not increase again until the next rainfall. sketch a graph to represent the scenario. label any maximum or minimum values. identify the intervals of increase and decrease.

Explanation:

Step1: Set up axes

Let the x - axis represent time and the y - axis represent the mosquito population.

Step2: Mark rainfall events

Mark the times of rainfall on the x - axis. Let's call the first rainfall time $t_1$ and the next rainfall time $t_2$.

Step3: Sketch increase

Right after $t_1$, draw a curve that goes up rapidly to represent the significant increase in the mosquito population.

Step4: Sketch decrease

After the peak, draw a curve that slopes down gradually until it reaches a horizontal line (sustainable level).

Step5: Identify intervals

The interval of increase is from $t_1$ until the time of the maximum population value. The interval of decrease is from the time of the maximum population value until the population reaches the sustainable level. The maximum value is the population value at the peak of the curve after the rainfall. There is no minimum value in the context of the described scenario other than the sustainable - level population value which is a horizontal asymptote of the decreasing part of the curve.

Answer:

The graph has an x - axis labeled 'Time' and a y - axis labeled 'Mosquito Population'. There are marked points for rainfall events. The curve increases rapidly after a rainfall, then decreases gradually to a sustainable level. The interval of increase is from the time of rainfall until the maximum population time. The interval of decrease is from the maximum population time until the population reaches the sustainable level. The maximum value is the population at the peak of the increase - curve after rainfall.