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