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# Although the model in Prob. 22.4 works adequately when population growth is unlimited

ISBN: 9780073401102 336

## Solution for problem 22.5 Chapter 22

Applied Numerical Methods W/MATLAB: for Engineers & Scientists | 3rd Edition

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Applied Numerical Methods W/MATLAB: for Engineers & Scientists | 3rd Edition

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Problem 22.5

Although the model in Prob. 22.4 works adequately when population growth is unlimited, it breaks down when factors such as food shortages, pollution, and lack of space inhibit growth. In such cases, the growth rate is not a constant, but can be formulated as kg = kgm(1 p/pmax ) where kgm = the maximum growth rate under unlimited conditions, p = population, and pmax = the maximum population. Note that pmax is sometimes called the carrying capacity. Thus, at low population density p pmax, kg kgm. As p approaches pmax, the growth rate approaches zero. Using this growth rate formulation, the rate of change of population can be modeled as dp dt = kgm(1 p/pmax)p This is referred to as the logistic model. The analytical solution to this model is p = p0 pmax p0 + (pmax p0)ekgm t Simulate the worlds population from 1950 to 2050 using (a) the analytical solution, and (b) the fourth-order RK method with a step size of 5 years. Employ the following initial conditions and parameter values for your simulation: p0 (in 1950) = 2,560 million people, kgm = 0.026/yr, and pmax = 12,000 million people. Display your results as a plot along with the data from Prob. 22.4.

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PY 205 Daniel Dougherty Week 2 Notes Chapter 3 - Kinematics in two or three dimensions  Vectors and scalars – velocity is how fast and in what direction the particle is moving o Magnitude – vector quantity o Scalar quantities are specified by numbers and units  Addition of vectors – graphical methods o  above D = displacement vectors...

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##### ISBN: 9780073401102

This textbook survival guide was created for the textbook: Applied Numerical Methods W/MATLAB: for Engineers & Scientists , edition: 3. Since the solution to 22.5 from 22 chapter was answered, more than 734 students have viewed the full step-by-step answer. The answer to “Although the model in Prob. 22.4 works adequately when population growth is unlimited, it breaks down when factors such as food shortages, pollution, and lack of space inhibit growth. In such cases, the growth rate is not a constant, but can be formulated as kg = kgm(1 p/pmax ) where kgm = the maximum growth rate under unlimited conditions, p = population, and pmax = the maximum population. Note that pmax is sometimes called the carrying capacity. Thus, at low population density p pmax, kg kgm. As p approaches pmax, the growth rate approaches zero. Using this growth rate formulation, the rate of change of population can be modeled as dp dt = kgm(1 p/pmax)p This is referred to as the logistic model. The analytical solution to this model is p = p0 pmax p0 + (pmax p0)ekgm t Simulate the worlds population from 1950 to 2050 using (a) the analytical solution, and (b) the fourth-order RK method with a step size of 5 years. Employ the following initial conditions and parameter values for your simulation: p0 (in 1950) = 2,560 million people, kgm = 0.026/yr, and pmax = 12,000 million people. Display your results as a plot along with the data from Prob. 22.4.” is broken down into a number of easy to follow steps, and 205 words. Applied Numerical Methods W/MATLAB: for Engineers & Scientists was written by and is associated to the ISBN: 9780073401102. This full solution covers the following key subjects: . This expansive textbook survival guide covers 24 chapters, and 496 solutions. The full step-by-step solution to problem: 22.5 from chapter: 22 was answered by , our top Engineering and Tech solution expert on 03/05/18, 09:01PM.

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