Revising the Predator-Prey Equations Consider a predatorprey relationship with x prey

Chapter 6, Problem 35

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Revising the Predator-Prey Equations Consider a predatorprey relationship with x prey and y predators at time t. Assume both predator and prey are present. Then the rates of change of each population can be modeled by the following revised predator-prey system of differential equations. Rate of change of prey population Rate of change of predator population (a) If there are no predators, the prey population will grow according to what model? (b) Write the revised predator-prey equations for and Find the critical numbers. (c) Use a graphing utility to graph the functions and of the revised predator-prey equations when and the initial conditions are and Describe the behavior of each solution as increases. (d) Use a graphing utility to graph a slope field of the revised predator-prey equations when and (e) Use the predator-prey equations and the slope field in part (d) to graph the solution curve using the initial conditions in part (c). Describe the changes in the prey and predator populations as you trace the solution curve.