Explanation Given: Total number of employee in office is N which is equal to 45. The number of initial persons who start the rumor y 0 is equal to 3. Approach: Use the logistic equation and its general solution to calculate the required parameter. Calculation: The spread rate of rumor is proportional to the multiplication of the number of people heard and number of people who do not heard the rumor is given by the logistic equation d y d t = k ( 1 − y N ) y , where y is the number of infected people at any time t , k is infection rate and N is the total population of the community. The general solution in terms of t of this logistic equation is the number of infected people at time t. The general solution for the logistic equation is, y = N 1 + b e − k t ... ( 1 ) , where b is equal to N − y 0 y 0 . To find the value of b, substitute the values of N and y 0 in the equation. b = 45 − 3 3 = 14 Put the values of N and b in the equation (1), y = 43 1 + 14 e − k t Now, put y equal to 12 and t equal to 3 to find the value of k To determine (b) To find: Time in which 30 employees heard the rumor.

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 11.6, Problem 7E

To determine

(a)

To find:

The equation which represents the number of persons who heard the rumor in t day.

To determine

(b)

To find:

Time in which 30 employees heard the rumor.

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Chapter 11.6, Problem 6E

Chapter 11.6, Problem 8E

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

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(a) To find: The equation which represents the number of persons who heard the rumor in t day.

Solution Summary: The author calculates the spread rate of rumor by using the logistic equation and its general solution.