Concept explainers
Oscillating growth rates Some species have growth rates that oscillate with an (approximately) constant period P. Consider the growth rate function
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 N(0) = 10, does the population ever become extinct? Explain.
- b. Suppose P = 10, A = 20, and r = 0. If the initial population is N(0) = 100, does the population ever become extinct? Explain.
- c. Suppose P = 10, A = 50, and r = 5. If the initial population is N(0) = 10, does the population ever become extinct? Explain.
- d. Suppose P = 10, A = 50, and r = −5. Find the initial population N(0) needed to ensure that the population never becomes extinct.
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