Solved: In Exercise 10 of Section 5.9, we considered the problem of predicting the

Chapter 10, Problem 11

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In Exercise 10 of Section 5.9, we considered the problem of predicting the population of two species that compete for the same food supply. In the problem, we made the assumption that the populations could be predicted by solving the system of equations dx1(t) dt = x1(t)(4 0.0003x1(t) 0.0004x2(t)) and dx2(t) dt = x2(t)(2 0.0002x1(t) 0.0001x2(t)). In this exercise, we would like to consider the problem of determining equilibrium populations of the two species. The mathematical criteria that must be satisfied in order for the populations to be at equilibrium is that, simultaneously, dx1(t) dt = 0 and dx2(t) dt = 0. This occurs when the first species is extinct and the second species has a population of 20,000 or when the second species is extinct and the first species has a population of 13,333. Can an equilibrium occur in any other situation?