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Phosphorus Pollution in a Shallow Lake

This worksheet involves a model for the phosphorus content in the water of a shallow lake. The x-axis shows the total stock of phosphorus in the lake water (in tons) and the y-axis is the flow rate of phosphorus (in tons per year). The outflow of phosphorus is proportional to the stock of phosphorus in the lake and is denoted by the green line. Phosphorus flows into the lake water from sediments at a rate that depends on the stock of phosphorus in the lake and from agricultural and residential pollution sources. The total inflow from these sources is denoted by the blue curve. The point A is an equilibrium where the inflow and outflow of phosphorus balance. The inflow of phosphorus from pollution sources can be adjusted with the slider from b=0 to b=50 tons per year. When b=0, there is no inflow from agricultural and residential pollution, and the total inflow is from lake sediments alone. When the stock of phosphorus is low (less than 75 kilograms) the lake is in an oligotrophic state characterized by high water quality. The lake is suitable for recreation and the oxygen rich water supports fish species popular with anglers. When the stock of phosphorus is high (greater than 150 kilograms) the lake is in a eutrophic state characterized by low water quality. The lake becomes dominated by algae that starves the water of oxygen making the lake unsuitable for fish and undesirable for water recreation.