Concept explainers
(a)
To find: the quadratic model for the data.
The quadratic model:
Given:
Price P | Number of books, n (in thousands) |
$10 | 900 |
$15 | 630 |
$20 | 396 |
$25 | 227 |
$30 | 102 |
$35 | 36 |
Calculation:
Here, use the quadratic regression function of your calculator, inputting the given data to find a quadratic model for it. Use the price, p as the "x" value, and Number of books, "n" as a y value. You should get the quadratic model:
Conclusion:
Therefore, the quadratic model:
(b)
To estimate: the slopes of the graph ad graph the model
The slope of the graph is
Calculation:
Graph the quadratic model you got in part (a). Now use this graph to estimate the slopes of the graph when
For
For
Conclusion:
Therefore,the slope of the graph is
(c)
To compare: the slopes given by the graphing utility and graph the tangent lines
Slopes are both fairly close to our approximations.
Calculation:
Using a graphing calculator to graph the tangent lines to the model at
Conclusion:
Therefore,slopes are both fairly close to our approximations.
(d)
To explain: about the tangent lines which are not same
The decline in number of books sold will be more subtle if they increase the price from $30 to a greater amount per book.
Calculation:
The slope of the tangent line at
Conclusion:
Therefore,the decline in number of books sold will be more subtle if they increase the price from $30 to a greater amount per book.
Chapter 11 Solutions
Precalculus with Limits: A Graphing Approach
- 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