   Chapter 11.2, Problem 60E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Spread of a rumor The number of people N ( t ) in a community who are reached by a particular rumor at time t (in days) is given by N ( t ) = 50 , 500 1 + 100 e − 0.7 t Find the rate of change of N ( t ) .

To determine

To calculate: Rate of change of N(t) where N(t)=50,5001+100e0.7t is a model for the number of people N(t) in a community who are reached by a particular rumor at time t (in days).

Explanation

Given Information:

The number of people N(t) in a community who are reached by a particular rumor at time t (in days) is represented by the function

N(t)=50,5001+100e0.7t

Formula used:

The rate of change is given by N(t).

Calculation:

Consider the provided function,

N(t)=50,5001+100e0.7t

Where, t is time (in days).

Differentiate both sides with respect to t,

N(t)=ddt(50,5001+100e0.7t)=50,500ddt(1+100e0.7t)1

Apply chain rule,

N(t)=50,500ddt(1+100e0.7t)1=50,500(1)(1+100e0.7t)11ddt(1+100e0.7t)=50,500(1+100e0.7t)2(0+100ddt(e0

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