Solved: 9396. Logistic growth Scientists often use the

Chapter 3, Problem 94

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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 1) The population of the world reached 6 billion in 1999 1t = 02. Assume Earths carrying capacity is 15 billion and the base growth rate is r0 = 0.025 per year. a. Write a logistic growth function for the worlds population (in billions) and graph your equation on the interval 0 t 200 using a graphing utility. b. What will the population be in the year 2020? When will it reach 12 billion?

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