here\'s the link to the answer with the graph, but I don\'t get which formulas i

Question

here's the link to the answer with the graph, but I don't get which formulas i should enter into my calculator to have the graph. please help!

http://www.chegg.com/homework-help/questions-and-answers/suppose-certain-population-growth-rate-varieswith-time-population-satisfies-differentialeq-q319539

Suppose that a certain population has a growth rate that varieswith time and that this population satisfies the differentialequation: dy / dt = (0.5 + sin t)y /5.
a) If y(0) = 1, find (or estimate) the time ? at which thepopulation has doubled. Choose other initial conditions anddetermine whether the doubling time ? depends on the initialpopulation.
b) Suppose that the growth rate is replaced by its average value1/10. Determine the doubling time ? in this case.
c) Suppose that the term sin t in the differentialequation is replaced by sin 2?t; that is, thevariation in the growth rate has a substantially higherfrequency. What effect does this have on the doubling time??
d) Plot the solutions obtained in parts (a), (b), and (c) on asingle set of axes.

Explanation / Answer

dy / dt = (0.5 + sin t)y /5 =>dy/y = 0.1dt + sintdt/5 =>lny = 0.1t-(cost/5)+C y(0) = 1 =>ln1 = 0.1*0 - (cos0/5) + C =>C = 1/5 =>lny = 0.1t-(cost/5)+(1/5) a)ln2 = 0.1t+0.2-(cost/5) =>t = 6.87

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