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.

Transcribed Image Text:

2mt N'(t) = r + A sin