a The figure below shows plots of the inflow and the outflow of phosphorus when the the pollution level P = 15 tons per year. (a) How many equilibrium points can you identify in the model? Label each point. It will be easiest if we agree to use letters A, B, ..., (b) At each dynamic equilibrium, estimate the stock of phosphorus in the lake (S) (this should be a different at each equilibrium). (c) Pick one equilibrium and label some value of the stock S that is near but not at that equilibrium (label it with an X your label should be on the horizontal axis). At your value of X determine which is larger: the inflow or the outflow? (d) Based on your answer to the previous question, what should happen to the stock of phosphorus in the lake when it is at X? Will it move toward or away from the nearby equilibrium value? (e) Determine which equilibria are stable and which are unstable. Flow rate (tons/yr) --- Outflow Inflow 150 100 ---- 50 Phosphorus (tons) 200 250 300 50 100 150 a The figure below shows plots of the inflow and the outflow of phosphorus when the the pollution level P = 15 tons per year. (a) How many equilibrium points can you identify in the model? Label each point. It will be easiest if we agree to use letters A, B, ..., (b) At each dynamic equilibrium, estimate the stock of phosphorus in the lake (S) (this should be a different at each equilibrium). (c) Pick one equilibrium and label some value of the stock S that is near but not at that equilibrium (label it with an X your label should be on the horizontal axis). At your value of X determine which is larger: the inflow or the outflow? (d) Based on your answer to the previous question, what should happen to the stock of phosphorus in the lake when it is at X? Will it move toward or away from the nearby equilibrium value? (e) Determine which equilibria are stable and which are unstable. Flow rate (tons/yr) --- Outflow Inflow 150 100 ---- 50 Phosphorus (tons) 200 250 300 50 100 150