Suppose that the growth of a population is described by N₍ₘ₊₁₎: = (1 + RₒΔt) N. •
where Rₒ< 0.
(a) Determine the population at later times, if initially the population isN₀
(b) Sketch the solution if - 1 < RₒΔt < 0.
(c) Sketch the solution if -2 < RₒΔt < -I: The result is called a convergent oscillation.
(d) Sketch the solution if RₒΔt < -2. The result is called a divergent
oscillation.
(e) Why are parts (c) and (d) not reasonable ecological growth models,
while part (b) is? What ecological assumption of the model caused
parts (c) and (d) to yield unreasonable results?