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The Gompertz differential equation N'it) = a\n-^Nit) serves as a model for the growth

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 14 Chapter 5.6

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 14

The Gompertz differential equation N'it) = a\n-^Nit) serves as a model for the growth oftumors where A(/) is the number of cells in a tumor at time t. The maximum number of cells that can be supported is K, and a is constant related to the proliferative ability of the cells. In a particular type of cancer, a = 0.0439, k = 12000, and I is measured in months. At the time (f = 0) the tumor is detected, A(0) = 4000. Using the Adams predictor-corrector method with h = 0.5, find the number of months it takes for N(t) = 11000 cells, which is the lethal number of cells for this cancer

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S343 Section 2.1 Notes- First Order Linear Equations and Integrating Factors 8-25-16  Recall equation for motion of falling object: = = − + o Position: = + + 2 0 0 o Velocity: = + 0  Replacing constants and with arbitrary functions of : = − + () o Arrive at general first order form + = ( )

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Chapter 5.6, Problem 14 is Solved
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Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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The Gompertz differential equation N'it) = a\n-^Nit) serves as a model for the growth