Animal populations are not capable of unrestricted growth because of limited habitat and food supplies Under such conditions the

Question

Animal populations are not capable of unrestricted growth because of limited habitat and food supplies Under such conditions the population follows a logistic growth model P t 1 ke ct where c d and k are positive constants For a certain fish population in a small pond d 1200 k 11 c 0 2 and t is measured in years The fish were introduced into the pond a How many fish were originally put in the pond 100 fish b Find the population after 10 20 and 30 years Round your answers to the nearest whole number 10 years 1057 X fish 20 years 1108 30 years 1197 c Evaluate P t for large values of t What value does the population approach as t P t 0 x Does the graph shown confirm your calculations P 1200 1000 800 600 X fish X fish 400 200

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