In the study of ecosystems, predator prey models are often used to study the interaction between species Consider populations of tundra wolves, given by W(t), and caribou, given by C(t), in northern Canada The interaction has been modeled by the equations (a) What values of dC dt and dW dt correspond to stable populations (b) How would the statement The caribou go extinct be represented mathematically (c) Suppose that a 0 05, b 0 001, c 0 05, and d 0 0001 Find all population pairs (C, W) that lead to stable populations According to this model, is it possible for the two species to live in balance or will one or both species become extinct dW cW dCW dt dC C bCW dr

Question: In the study of ecosystems, predator-prey models are often used to study the interaction between species. Consider populations of tundra wolves, given by W(t), and

In the study of ecosystems, predator-prey models are often used to study the interaction between species. Consider populations of tundra wolves, given by W(t), and caribou, given by C(t), in northern Canada. The interaction has been modeled by the equations

(a) What values of dC/dt and dW/dt correspond to stable populations?
(b) How would the statement €œThe caribou go extinct€ be represented mathematically?
(c) Suppose that a = 0.05, b = 0.001, c = 0.05, and d = 0.0001. Find all population pairs (C, W) that lead to stable populations. According to this model, is it possible for the two species to live in balance or will one or both species become extinct?

dW -cW + dCW dt dC C- bCW dr

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