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Name:Math 5B - Calculus for Life Sciences II7.5, 7.6 - Written Homework due Thur, Feb 25 at 10pmInstructions:In the space below, answer the following questions,showing all your work.Be sure toput a BOX around your final answer.Scan/upload your solutions via Canvas by Thur, Feb 25 at10pm.1. Systems of di↵erential equations are useful for modeling how the population of two species (usually apredator and prey) influence each other. Below are modified Lotka-Volterra equations modeling thepopulation of wolves (W) and rabbits (R).dRdt=0.08R(1-0.0002R)-0.001RWdWdt=-0.02W+ 0.00002RW(a) In the absence of wolves (i.e., whenW= 0), what does the model say happens to the rabbitpopulation? To figure this out, analyzedRdtwhenW= 0. Notice you’ll get a regular autonomousdi↵erential equation forR. What are its equilibria? Are they locally stable or unstable? Whatdoes that mean in terms of the rabbit population in the absence of wolves?(b) In the absence of rabbits (i.e., whenR= 0), what does the model say happens to the wolfpopulation? Similar to the above, analyze