how to use MATLAB to solve; Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy/dt= (0.5 + sint)y/2.

a. If y(0) = 1, find (or estimate) the timeat which the population has doubled. Choose otherinitial conditions and determine whether the doubling time ? depends on the initial population.

b. Suppose that the growth rate is replaced by its average value 1/4. Determine the doubling timein this case.

c. Suppose that the term sin t 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 ?

d. Plot the solutions obtained in parts (a), (b), and (c) on a single set of axes.