Concept explainers
a.
To find: an exponential model and a power model for the data and identify the coefficient of determination for each model using the regression feature of a graphing utility.
a.
Answer to Problem 29E
Exponential model:
Power model:
Explanation of Solution
Given information: The table shows the yearly sales estimates S (in billions of dollars).
for the online grocery shopping market for the years 2012 through 2018.
Year | Sales, S (in billions) |
2012 | 6.0 |
2013 | 6.9 |
2014 | 8.4 |
2015 | 10.1 |
2016 | 12.0 |
2017 | 14.2 |
2018 | 17.5 |
Calculation:
Let t represent the year, with t = 2 corresponding to 2012 ,then the above data table can be written as below.
Year | Sales, S (in billions) |
2 | 6.0 |
3 | 6.9 |
4 | 8.4 |
5 | 10.1 |
6 | 12.0 |
7 | 14.2 |
8 | 17.5 |
Using the graphing utility, the exponential model of the above table data is:
Using the graphing utility, the power model of the above table data is:
b.
To graph: each model with the data using the graphing utility.
b.
Answer to Problem 29E
Explanation of Solution
Given information: Exponential model:
Power model:
Calculation:
The graph of Exponential model:
The graph of Power model:
c.
To find: which model fits the data better.
c.
Answer to Problem 29E
The exponential model fits the data better because
Explanation of Solution
Given information:
Calculation:
The exponential model fits the data better because
Chapter 3 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