Concept explainers
a.
To find: a quadratic model for the data using the regression feature of a graphing utility.
a.
Answer to Problem 68E
Explanation of Solution
Given information: The table shows the number N ( in thousands) of books sold when the price per book is p (in dollars).
Price p (in dollars) | Number of books, n (in thousands) |
10 | 900 |
15 | 630 |
20 | 396 |
25 | 227 |
30 | 102 |
35 | 36 |
Calculation:
Using the regression feature of a graphing utility, the quadratic model for the above table data is:
b.
To graph: the model found in part (a) using the graphing utility and estimate the slope of the graph when p = 15 and p = 30.
b.
Answer to Problem 68E
The slope of the graph when:
Explanation of Solution
Given information:
Calculation:
The graph of the model
From the graph
c.
To graph: the tangent lines to the model when p = 15 and p = 30. And compare the slope given by the graphing utility with estimates in part (b)
c.
Answer to Problem 68E
f’ (15) = -50.3 and f’ (30) = -19.1.
Explanation of Solution
Given information:
Calculation:
Using a graphing calculator to graph the tangent lines to the model at p = 15 and p = 30, get f’ (15) = -50.3 and f’ (30) = -19.1, which are both fairly close to our approximations.
d.
To explain: the slope of the tangent lines at p = 15 and p = 30 are not the same, what this means to the company selling the books.
d.
Explanation of Solution
Given information:
Calculation:
The slope of the tangent line at p = 15 has a far more negative slope than that at p = 30. This means that the company will see a more radical decline in number of books sold as they increase the price past $15 per book, but that 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 W/LIMITS:GRAPH.APPROACH(HS)
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning