Concept explainers
a.
To calculate: The linear model
a.
Answer to Problem 60E
The linear model
Explanation of Solution
Given information:
The time measured in seconds required by a car to attain a speed measured in miles from a starting point is provided below,
Also, the above data can be modeled as,
Calculation:
Consider the time measured in seconds required by a car to attain a speed measured in miles from a starting point is provided below,
Follow the steps provided below to estimate the linear model.
Step 1: Press
Step 2: Press
Step 3: Enter the column 1 of table provided above in
Step 4: Enter the column 2 of table provided above in
Step 5: Press
Step 6: Press
Step 7: Select the fourth option that is
Step 8: Press
Step 9: Press
The result obtained on screen is provided below.
Therefore, linear model is,
Follow the steps provided below to estimate the exponential model.
Step 1: Press
Step 2: Press
Step 3: Enter the column 1 of table provided above in
Step 4: Enter the column 2 of table provided above in
Step 5: Press
Step 6: Press
Step 7: Select the fourth option that is
Step 8: Press
Step 9: Press
The result obtained on screen is provided below.
Therefore, exponential model is,
b.
To graph: The model that represent the data.
b.
Explanation of Solution
Given information:
The time measured in seconds required by a car to attain a speed measured in miles from a starting point is provided below,
Also, the above data can be modeled as,
Graph:
Consider the time measured in seconds required by a car to attain a speed measured in miles from a starting point is provided below,
Also, the above data can be modeled as,
The linear model
Plot the data points and all the models in the coordinate plane.
The green curve line represents
Interpretation:
All the models and the data points itself coincide with each other. All the models fits with the data.
c.
To calculate: The tabular estimation of the models for the data.
c.
Answer to Problem 60E
The estimation is provided below,
Explanation of Solution
Given information:
The time measured in seconds required by a car to attain a speed measured in miles from a starting point is provided below,
Also, the above data can be modeled as,
Calculation:
Consider the time measured in seconds required by a car to attain a speed measured in miles from a starting point is provided below,
The linear model
For each value of s compute the value of t for different models.
d.
To calculate: The sum of absolute values of differences between data and estimated values provided by each model. Also explain the model that best fits the data based on sums.
d.
Answer to Problem 60E
The sum is
Explanation of Solution
Given information:
The time measured in seconds required by a car to attain a speed measured in miles from a starting point is provided below,
Also, the above data can be modeled as,
Calculation:
Consider the time measured in seconds required by a car to attain a speed measured in miles from a starting point is provided below,
Also, the above data can be modeled as,
The linear model
For each value of s compute the value of t for different models.
Now, sum of absolute values of differences between data and estimated values provided by each model is,
For
For
For
For
The model that best fits the data is the one which has least sum of the absolute values of the differences between the estimated and actual data. This is represented by model
Thus, the sum is
Chapter 3 Solutions
EBK PRECALCULUS W/LIMITS
- 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