Official Explanation
1. Based on the information provided, which one of the following was the team’s estimate of KJR’s fish population?
To find the team’s estimate of the fish population, insert the given data into the equation provided in the second tab, where M is the number of fish in the capture group (60), N is the number of fish in the recapture group (100), 5 fish are common to both groups, and P is the estimated fish population: 5/100=60/P. Cross-multiply to get 5P = 6,000. Divide both sides of the equation by 5 to get P = 1,200.
The correct answer is 1,200.
2. For each of the following scenarios, select Restock if the scenario would indicate that the team will need to restock the reservoir. Otherwise, select Do not restock.
Insert the given data into the equation provided, where M is the number of fish in the capture group (60), N is the number of fish in the recapture group (60), and P is the total fish population: (number of fish common to both groups)/(P)=60/P. Cross-multiplying gives P(number of fish common to both groups)= 3,600. Isolating P gives P=3600/(number of fish common to both groups). If P is less than 1,500, the information in the discussion indicates that the team will need to restock the lake.
RO1
From the analysis above, P=3,600/2= 1,800. This number is not less than 1,500, so the team will not need to restock the lake.
The correct answer is Do not restock.
RO2
From the analysis above, P=3,600/4=900. This number is less than 1,500, so the team will need to restock the lake.
The correct answer is Restock.
RO3
From the analysis above, P=3,600/6=600. This number is less than 1,500, so the team will need to restock the lake.
The correct answer is Restock.
3. Assume that at the beginning of next year’s fishing season the fish population will be at the minimum level for the start of the fishing season. For each of the following numbers of fish removed from KJR during that fishing season, select Yes if the model for population increase predicts that the fish population will increase by at least 40 fish due to reproduction. Otherwise, select No.
The Discussion indicates that the fish’s population should be no less than 1,500 at the start of the fishing season. Therefore, at the end of that season (the start of September), the population P will be 1,500 minus the number of fish removed during the season. With this number, the graph provided can then be used to predict the increase in the fish population due to reproduction.
RO1
P=1,500−100=1,400. According to the graph, a P of 1,400 is predicted to increase by slightly more than 40 fish.
The correct answer is Yes.
RO2
P=1,500−200=1,300. According to the graph, a P of 1,300 is predicted to increase by approximately 45 fish.
The correct answer is Yes.
RO3
P=1,500−600=900. According to the graph, a P of 900 is predicted to increase by approximately 50 fish.
The correct answer is Yes.