   Chapter 3.4, Problem 84E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Under certain circumstance a rumor spreads according to the equation p ( t ) = 1 1 + a e − k t where p(t) is the proportion of the population that has heard the rumor at time t and a and k are positive constants. [In Section 9.4 we will see that this is a reasonable equation for p(t).](a) Find limt→∞ p(t).(b) Find the rate of spread of the rumor.(c) Graph p for the case a= 10, k = 0.5 with 1 measured in hours. Use the graph to estimate how long it will take for 80% of the population to hear the rumor.

(a)

To determine

To find: The limit of the function limtp(t).

Explanation

Calculation:

Obtain limit of the function.

That is, compute limtp(t).

limtp(t)=limt(11+aekt)=limt(11+aekt<

(b)

To determine

To find: The rate of spread of the rumor.

(c)

To determine

To sketch: The graph p(t) and estimate the time such that 80% of the population to hear the rumor.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 516, evaluate the given quantity. log42

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Define sampling with replacement and explain why is it used?

Statistics for The Behavioral Sciences (MindTap Course List)

#### Name each polygon:

Elementary Technical Mathematics

#### Factor completely. x+2xy

Trigonometry (MindTap Course List)

#### In Exercise 724, Compute the indicated products. 3

Finite Mathematics for the Managerial, Life, and Social Sciences

#### For f(x) = 3x + 1 and g(x) = x, ?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 