Answer: 9396. Logistic growth Scientists often use the

Chapter 3, Problem 95

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9396. Logistic growth Scientists often use the logistic growth function P1t2 = P0 K P0 + 1K - P02e-r0t to model population growth, where P0 is the initial population at time t = 0, K is the carrying capacity, and r0 is the base growth rate. The carrying capacity is a theoretical upper bound on the total population that the surrounding environment can support. The figure shows the sigmoid (S-shaped) curve associated with a typical logistic model. World population (part 2) The relative growth rate r of a function f measures the rate of change of the function compared to its value at a particular point. It is computed as r1t2 = f _1t2>f 1t2. a. Confirm that the relative growth rate in 1999 1t = 02 for the logistic model in Exercise 94 is r102 = P _102>P102 = 0.015. This means the worlds population was growing at 1.5% per year in 1999. b. Compute the relative growth rate of the worlds population in 2010 and 2020. What appears to be happening to the relative growth rate as time increases? c. Evaluate lim tS_ r1t2 = lim tS_ P _1t2 P1t2 , where P1t2 is the logistic growth function from Exercise 94. What does your answer say about populations that follow a logistic growth pattern?