Concept explainers
a.
To find: a quadratic model for the data using the regression feature of a graphing utility.
a.
Answer to Problem 67E
Explanation of Solution
Given information: The table shows the revenues y (in billions of dollars) for Goodyear
Tire & Rubber from 2011 through 2017.
Year t | Revenue , y (in billions of dollars) |
2011 | 22.77 |
2012 | 20.99 |
2013 | 19.54 |
2014 | 18.14 |
2015 | 16.44 |
2016 | 15.16 |
2017 | 15.38 |
Calculation:
Let t represents the year, with t = 1 corresponding to 2011, so above table can be written as:
Year t | Revenue , y (in billions of dollars) |
1 | 22.77 |
2 | 20.99 |
3 | 19.54 |
4 | 18.14 |
5 | 16.44 |
6 | 15.16 |
7 | 15.38 |
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 t = 4 and interpret the result.
b.
Answer to Problem 67E
The slope at t =4 is about -1.34. In 2014, revenue for Goodyear Tire & Rubber was decreasing by about $1.34 billion per year.
Explanation of Solution
Given information:
Calculation:
The graph of the model
The slope at t =4 is about -1.34. In 2014, revenue for Goodyear Tire & Rubber was decreasing by about $1.34 billion per year.
c.
To find: the derivative of the model in part (a) and then evaluate the derivative for t = 4.
c.
Answer to Problem 67E
Explanation of Solution
Given information:
Calculation:
Chapter 11 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- 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