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5. -/1 points HunterDM3 6.4.006b.Consider the following discrete-time population model:Pn = A if n = 0 r(1 - Pn-1) if n > 0Both the initial population A and the parameter r are between 0 and 1, noninclusive.Let x∞ be the fixed point of the function f(x) = r(1 - x), where 0 < r < 1. Prove thatPn-1≥ x∞ Pn ≤ x∞ and Pn-1≤ x∞ Pn ≥ x∞.This answer has not been graded yet.eBook
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In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation (d P)/(d t)=P(a-b P), where a and b are positive constants. Although we will come back to this equation and solve it by an alternative method in Section 3.2, solve the DE this first time using the fact that it is a Bernoulli equation. | Numerade
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