HW_Feb_25.pdf - maleinabahilig Name Math 5B Calculus for...

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Name: Math 5B - Calculus for Life Sciences II 7.5, 7.6 - Written Homework due Thur, Feb 25 at 10pm Instructions: In the space below, answer the following questions, showing all your work. Be sure to put a BOX around your final answer. Scan/upload your solutions via Canvas by Thur, Feb 25 at 10pm. 1. Systems of di erential equations are useful for modeling how the population of two species (usually a predator and prey) influence each other. Below are modified Lotka-Volterra equations modeling the population of wolves (W) and rabbits (R). dR dt = 0 . 08 R (1 - 0 . 0002 R ) - 0 . 001 RW dW dt = - 0 . 02 W + 0 . 00002 RW (a) In the absence of wolves (i.e., when W = 0), what does the model say happens to the rabbit population? To figure this out, analyze dR dt when W = 0. Notice you’ll get a regular autonomous di erential equation for R . What are its equilibria? Are they locally stable or unstable? What does that mean in terms of the rabbit population in the absence of wolves? (b) In the absence of rabbits (i.e., when R = 0), what does the model say happens to the wolf population? Similar to the above, analyze

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