Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy y (0.5 sint) + dt NOTE: Round your answers to two decimal places. = 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 = The doubling time does not depend on the initial population. b) Suppose that the growth rate is replaced by its average value Determine the doubling time 7 in this case. In this case, T = 1 10 c) Suppose that the term sint in the differential equation is replaced by sin(2t); that is, the variation in the growth rate has a substantially higher frequency. What effect does this have on the doubling time 7? In this case, T =