Two separate rabbit populations are observed for 80 weeks, starting at the same time and with the same initial populations. The growth rates of two rabbit populations are modeled as follows, where t =0 corresponds to the beginning of the observation period:

Question

r1(t)=4sin((2pi/72)(t)) +.1t+1, where r(1) is rabbits/week, t is time in weeks
r2(t)=t^(1/2) , where r (2) is rabbits per week, t is time in weeks

a. Using your calculator, find (approximately) the first positive time t for which the rates of
growth for the two populations are the same
b. What’s the physical significance of the area between the two curves from time t = 0 until
the first time where the two rates are the same? What does the area represent?
c. Suppose you want to find the first time (call it T) after the beginning of the observation
period at which the two rabbit populations have identical populations. Write an equation to solve for the unknown variable T.
d.Simplify your equation from part C until you can use your calculator on it. Then use your calculator to solve this equation for T.

Answer 1

a. t=31.718 weeks (where the two lines intersect)
b. this is basically r1's accumulated population-r2's accumulated population, or how many more rabbits r1 has accumulated over the period of time.