Oscillating growth rates Some species have growth rates
Chapter 6, Problem 66(choose chapter or problem)
Oscillating growth rates Some species have growth rates that oscillate with an (approximately) constant period P. Consider the growth rate function N_1t2 = r + A sin 2pt P where A and r are constants with units of individuals>yr, and t is measured in years. A species becomes extinct if its population ever reaches 0 after t = 0. a. Suppose P = 10, A = 20, and r = 0. If the initial population is N102 = 10, does the population ever become extinct? Explain. b. Suppose P = 10, A = 20, and r = 0. If the initial population is N102 = 100, does the population ever become extinct? Explain. c. Suppose P = 10, A = 50, and r = 5. If the initial population is N102 = 10, does the population ever become extinct? Explain. d. Suppose P = 10, A = 50, and r = -5. Find the initial population N102 needed to ensure that the population never becomes extinct.
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