(a) Explanation Given: The Differential equation is R ( m ) = − r M ln ( M K ) , M ( 0 ) = M 0 (1) Graph: The graph of the growth rate function for R ( m ) = − r M ln ( M K ) is shown below in Figure 1. From Figure 1, it is observed that the above graph is the growth rate function of R ( m ) = − r M ln ( M K ) where the growth is increasing at particular value. Calculation: Consider R ( M ) = − r M ln ( M K ) , M ( 0 ) = M 0 . R ′ ( m ) = − r M ln ( M K ) = − r ( M ln M K ) = − r ( ln M K + M ⋅ K m ⋅ 1 k ) = − r ( ln M K ) + 1 (b) To determine To Solve: The given initial value problem with its solution graph and describe the growth pattern of the tumor as well as give comment if not find the limiting size of the tumor. (c) To determine To Describe: The meaning of K .

2nd Edition

ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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Differential Equations

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Chapter D1.3, Problem 49E

(a)

To determine

To sketch: The graph of the growth rate function and obtain the value of M such that the growth is positive as well as maximum.

(b)

To determine

To Solve: The given initial value problem with its solution graph and describe the growth pattern of the tumor as well as give comment if not find the limiting size of the tumor.

(c)

To determine

To Describe: The meaning of K.

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Chapter D1.3, Problem 48E

Chapter D1.3, Problem 50E

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The graph of the growth rate function and obtain the value of M such that the growth is positive as well as maximum.

Solution Summary: The author illustrates the graph of the growth rate function for R(m)=-rMmathrm

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To sketch: The graph of the growth rate function and obtain the value of M such that the growth is positive as well as maximum.

To Solve: The given initial value problem with its solution graph and describe the growth pattern of the tumor as well as give comment if not find the limiting size of the tumor.

To Describe: The meaning of K.

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Chapter D1 Solutions