Suppose that a lake is stocked with N fish of the same age, and that M is the mortality rate of the fish (the fraction of the fish that will die of natural causes during the year), and F is the fishing rate (the fraction that will be caught commercially). Then the number of fish C that will be caught during the year is given by the formula C=FN/ M+F; in this formula, M and F must be entered as decimal values. (a) Suppose that the lake is stocked with 5500 catfish at the beginning of the season and that the fish have a 7% mortality rate. If the catfish are removed at a fishing rate of 25%, what are the appropriate values of the quantities N, M and F in this situation? Use these to determine how many catfish will be caught by fishing from the lake. (b) Treat N and M as parameters with the same values given above. Then complete this table of function values of C in terms of F : (c) If this function C = C(F) were graphed, would it be an increasing or decreasing function? Would it be concave up or concave down?
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Suppose that a lake is stocked with N fish of the same age, and that M is the mortality rate of the fish (the fraction of the fish that will die of natural causes during the year), and F is the fishing rate (the fraction that will be caught commercially). Then the number of fish C that will be caught during the year is given by the formula
C=FN/ M+F;
in this formula, M and F must be entered as decimal values.
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(a) Suppose that the lake is stocked with 5500 catfish at the beginning of the season and that the fish have a 7% mortality rate. If the catfish are removed at a fishing rate of 25%, what are the appropriate values of the quantities N, M and F in this situation? Use these to determine how many catfish will be caught by fishing from the lake.
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(b) Treat N and M as parameters with the same values given above. Then complete this table of function values of C in terms of F :
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(c) If this function C = C(F) were graphed, would it be an increasing or decreasing function? Would it be concave up or concave down?
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