Concept explainers
(a)
To find: The limit of the function
(a)
Answer to Problem 74E
The limit of the function
Explanation of Solution
Calculation:
Obtain limit of the function.
That is, compute
Simplify further,
Therefore, the limit of the function
(b)
To find: The rate of spread of the rumor.
(b)
Answer to Problem 74E
The rate of spread of the rumor is
Explanation of Solution
Given:
The circumstances a rumor spreads according to the equation
Derivative rule:
Calculation:
Obtain the derivative of
Apply quotient rule (1),
Therefore, the rate of spread of rumor is
(c)
To sketch: The graph
(c)
Answer to Problem 74E
Use online graphing calculator and the draw graph of
The rumor spread 80% of the population when
Explanation of Solution
Calculation:
Consider
Substitute
Use online graphing calculator and the draw graph of
Zooms the graph towards the population
From Figure 2,it is observed that the rumor spread 80% of the population approximately when
Obtain time t when
Substitute
Take natural logarithm on both sides,
Therefore, the rumor spread 80% of the population when
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning