Concept explainers
(a)
To find: The rate at which the rate of change of the area within the circle is increasing after 1 s.
(a)
Answer to Problem 14E
The rate at which the rate of change of the area within the circle is increasing after 1 s is,
Explanation of Solution
Given:
A stone which is dropped into a lake that creates a circular ripple whose speed when it travels outward is 60 cm/s.
Calculation:
Area inside the ripple at time t is
That is,
The rate of change of the ripple at time t is,
Therefore, the rate at which the rate of change of the area within the circle is increasing after 1 s is,
(b)
To find: The rate at which the rate of change of the area within the circle is increasing after 3 s.
(b)
Answer to Problem 14E
The rate at which the rate of change of the area within the circle is increasing after 3 s is,
Explanation of Solution
From part (a), the rate of change of the ripple at time t is,
Therefore, the rate at which the rate of change of the area within the circle is increasing after 3 s is,
(c)
To find: The rate at which the rate of change of the area within the circle is increasing after 5 s. What can be concluded from the parts (a), (b) and (c).
(c)
Answer to Problem 14E
The rate at which the rate of change of the area within the circle is increasing after 5 s is,
Explanation of Solution
From part (a), the rate of change of the ripple at time t is,
Therefore, the rate at which the rate of change of the area within the circle is increasing after 5 s is,
From the parts (a), (b) and (c), it can be concluded that the rate of change increases as time increases.
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