Rabbit Overpopulation Problem: Figure 7-6e shows two logistic functions Both represent

Chapter 7, Problem 6

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Rabbit Overpopulation Problem: Figure 7-6e shows two logistic functions Both represent the population of rabbits in a particular woods as a function of time x in years. The value of the constant a is to be determined under two different initial conditions. Figure 7-6e a. For y = f(x) in Figure 7-6e, 100 rabbits were introduced into the woods at time x = 0. Find the value of the constant a under this condition. Show that your answer is correct by plotting the graph of f on your grapher. b. How do you interpret this mathematical model with regard to what happens to the rabbit population under the conditions in part a? c. For y = g(x) in Figure 7-6e, 2000 rabbits were introduced into the woods at time x = 0. Find the value of a under this condition. Show that the graph agrees with Figure 7-6e. d. How do you interpret the mathematical model under the condition of part c? What seems to be the implication of trying to stock a region with a greater number of a particular species than the region can support?

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