Concept explainers
(a)
To sketch: The scatter plot of the data point
(a)
Explanation of Solution
Given:
The data is as shown below.
|
|
2 | 0.08 |
4 | 0.12 |
6 | 0.18 |
8 | 0.25 |
10 | 0.36 |
12 | 0.52 |
14 | 0.73 |
16 | 1.06 |
The scatter plot of the data
Form Figure 1, it is noticed that the scatter plot of the data
(b)
To sketch: The scatter plots of
(b)
Explanation of Solution
Given:
|
|
2 | 0.08 |
4 | 0.12 |
6 | 0.18 |
8 | 0.25 |
10 | 0.36 |
12 | 0.52 |
14 | 0.73 |
16 | 1.06 |
The table of
|
|
|
|
2 | 0.08 | 0.69315 | -2.52573 |
4 | 0.12 | 1.38629 | -2.12026 |
6 | 0.18 | 1.79176 | -1.7148 |
8 | 0.25 | 2.07944 | -1.38629 |
10 | 0.36 | 2.30259 | -1.02165 |
12 | 0.52 | 2.48491 | -0.65393 |
14 | 0.73 | 2.63906 | -0.31471 |
16 | 1.06 | 2.77259 | 0.05827 |
Use online graphing calculator and draw the scatter plot of “
From Figure 2, it is noticed that the scatter plot of “
On the same manner, use online graphing calculator and draw the scatter plot of “
From Figure 3, it is noticed that the scatter plot of “
(c)
To find: The function which is more appropriate for modeling of this data, exponential or power function.
(c)
Explanation of Solution
The exponential function
Use online graphing calculator and draw graph of exponential function and power function on the scatter plot as shown below in Figure 4.
In Figure 4, the black line curve represents the exponential
From Figure 4, it is also noticed that the exponential curve
Therefore, the exponential function
(d)
To find: The appropriate function to model the data.
(d)
Answer to Problem 9P
The exponential model
Explanation of Solution
Given:
The data is listed as follows.
|
|
2 | 0.08 |
4 | 0.12 |
6 | 0.18 |
8 | 0.25 |
10 | 0.36 |
12 | 0.52 |
14 | 0.73 |
16 | 1.06 |
From part (c), in the Figure 4, it is noticed that the exponential function of the form
Therefore, the exponential model
Chapter 4 Solutions
Precalculus: Mathematics for Calculus - 6th 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