Concept explainers
a
To draw
a
Explanation of Solution
Given information:
Graph:
Interpretation:
Using a graphic utility, the scatter plot for the given data is shown above.
b
To find if the scatter plot could be modeled by linear model, quadratic model or neither.
b
Answer to Problem 15E
Quadratic model
Explanation of Solution
Given information:
To determine if the given graph can be modeled by linear model, quadratic model or neither of them, try to draw a straight line or a parabola through the given scatter plot.
If a straight line can be drawn through the points of the scatter plot, it could be modelled by linear model whereas if a parabola can be drawn through the points of the scatter plot, it could be modelled by a quadratic model.
In case if both are not possible, it could neither be modeled.
Here, in the given graph we could draw a parabola opened upwards. Therefore, the scatter plot could be modeled by a quadratic model.
Conclusion:
Therefore, given scatter plot is modeled by quadratic model.
c
To find a model for the data using regression feature of a graphing utility.
c
Answer to Problem 15E
Quadratic model
Explanation of Solution
Given information:
Calculation:
Using the graphic utility to find the regression,
Conclusion:
Therefore, from the above figure. the regression equation for the quadratic model is
d
To draw the model with the scatter plot from subpart (a) using a graphic utility.
d
Explanation of Solution
Given information:
Graph:
Interpretation:
Using a graphic utility, a parabola is formed when the data is kept on a graph.
e
To draw a table comparing the original data with the data given by the model.
e
Explanation of Solution
Given information:
Table:
Draw the table comparing the original data and the data given by the model.
Original data | Data from the model | ||
x | y | ||
0 | 587 | 0 | 591.497 |
5 | 551 | 5 | 590.6885 |
10 | 512 | 10 | 596.8311 |
15 | 478 | 15 | 609.9247 |
20 | 436 | 20 | 629.9694 |
25 | 430 | 25 | 656.9651 |
30 | 424 | 30 | 690.9119 |
35 | 420 | 35 | 731.8097 |
40 | 423 | 40 | 779.6586 |
45 | 429 | 45 | 834.4585 |
50 | 444 | 50 | 896.2095 |
Data from the model is obtained by substituting the values of x as
Interpretation:
When the original data and the data from the model are compared with each other, it is found that the values are nearly equal.
Chapter 2 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