In Problems 11–20, the given logistic differential equation models the rate of change of a population P with respect to time t. For each differential equation, find (a) the carrying capacity M. (6) the maximum population growth rate k. C) the population when P is growing most rapidly. (a (E dP dP 11. = 0.12P dt 12. =0.03 P 1- %3D 1 1000 dt 570 33. S d P 14. dt PAGE dP 13, = 0.25 P dt 0.08P 563 1600 4000 P dP 15. = 0.002P dt d P 16. = 0.005 P (1 15,000 1 2800 dt

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