Explanation Write the logistic equation for the given rumor and then determine the value of the constants with the initial values given to determine the solution. Given: A simpler model for the spread of a rumor assumes that the rate at which the rumor spreads is proportional (with factor k ) to the fraction of the population that has not yet heard the rumor. Calculation: Let y ( t ) be the fraction of population that has heard the rumor and given that the rumor spreads at a rate proportional (with factor k ) to the fraction of the population that has not yet heard the rumor. Hence, the rate is given by d y d t = k ( 1 − y ) Separating the variables and integrating gives ∫ d y ( 1 − y ) = ∫ k d t = > k t + C = − ln | 1 − y | = > y ( t ) = 1 − A e − k t where A = ± A e − C is a constant... To determine (b) Graph the two solutions on the same axis. To determine (c) Which model seems more realistic and why.

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.4, Problem 10E

To determine

(a)

The solutions to this model and the model of Exercise 8 with the values $k = 0.9, y_{0} = 0.1$ .

To determine

(b)

Graph the two solutions on the same axis.

To determine

(c)

Which model seems more realistic and why.

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Chapter 10.4, Problem 9E

Chapter 10.4, Problem 11E

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(a) The solutions to this model and the model of Exercise 8 with the values k = 0.9 , y 0 = 0.1 .

Solution Summary: The author explains the logistic equation for the spread of a rumor and the value of the constants with the initial values to determine the solution.

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(a)

The solutions to this model and the model of Exercise 8 with the values $k = 0.9, y_{0} = 0.1$ .

(b)

Graph the two solutions on the same axis.

(c)

Which model seems more realistic and why.

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Chapter 10 Solutions

(a) The solutions to this model and the model of Exercise 8 with the values k = 0.9 , y 0 = 0.1 .

Solution Summary: The author explains the logistic equation for the spread of a rumor and the value of the constants with the initial values to determine the solution.

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(a) The solutions to this model and the model of Exercise 8 with the values k=0.9,y0=0.1.

(b) Graph the two solutions on the same axis.

(c) Which model seems more realistic and why.

Want to see the full answer?

Chapter 10 Solutions

(a)

The solutions to this model and the model of Exercise 8 with the values $k = 0.9, y_{0} = 0.1$ .

(b)

Graph the two solutions on the same axis.

(c)

Which model seems more realistic and why.