Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy dt NOTE: Round your answers to two decimal places. = (0.5+ sin t) 5 a) If y(0) = 1, find (or estimate) the time 7 at which the population has doubled. Choose other initial conditions and determine whether the doubling time 7 depends on the initial population. The doubling time is 7 = 3 X The doubling time does not depend on the initial population. 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time in this case. In this case, T = 6.93 c) Suppose that the term sint in the differential equation is replaced by sin(2nt); that is, the variation in the growth rate has a substantially higher frequency. What effect does this have on the doubling time T? In this case, T = 6.8459 X Edit

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