Explanation Given: Total number of employee in office N is equal to 200. The number of initial persons who start the rumor y 0 is equal to 10 and in 10 days 35 people heard the rumor. Calculation: The rate of spread of 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 constant and N is the total population of the office. The general solution in terms of t of this logistic equation is the number of people who heard the rumor 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 = 200 − 10 10 = 19 Put the values of N and b in the equation (1) y = 200 1 + 19 e − k t Now, apply the condition, 35 people heard the rumor in 10 days. Put y equal to 35 and t equal to 3 to find the value of k . To determine (b) To find: The number of people who heard the rumor in 5 days.

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.CR, Problem 69CR

To determine

(a)

To find:

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

To determine

(b)

To find:

The number of people who heard the rumor in 5 days.

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Chapter 11.CR, Problem 68CR

Chapter 11.CR, Problem 70CR

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

Ch. 11.1 - YOUR TURN 1 Find all solutions of the differential...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - YOUR TURN In Example 6, find the goat population...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 2E Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E

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

Solution Summary: The author explains the logistic equation for the number of people who heard the rumor in t days.