Concept explainers
Demand for Soft Drinks A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table.
(a) Make a
(b) Find and graph a linear function that models the data.
(c) Use the model to predict soft drink sales if the temperature is 95°F.
High temperature (°F) | Number of cans sold |
55 | 340 |
58 | 335 |
64 | 410 |
68 | 460 |
70 | 450 |
75 | 610 |
80 | 735 |
84 | 780 |
(a)
To graph: The scatter plot of the data.
Explanation of Solution
Graph:
Consider the High temperature as the x coordinates and number of cans sold as the y coordinates.
The scatter plots of the given data are shown below in Figure 1.
From Figure 1, all the points are plotted on the graph. No two points coincide each other.
(b)
To find: The linear function that represents the given data and draw the graph for it.
Answer to Problem 2P
The linear function that represents the given data is
Explanation of Solution
Using the online calculator, the regression line for the given data obtained is
The above regression line is in the form of linear equation.
Therefore, the linear function that represents the given data is
The graph that represents the equation
From Figure 2, the graph for the linear equation
(c)
To find: The number of soft drink sold if the temperature is
Answer to Problem 2P
The number of soft drink sold if the temperature is
Explanation of Solution
Consider the temperature is
From part (b), it is obtained that the linear equation that represents the given data is
Substitute x = 95 in the above equation to compute the number of cans sold.
Thus, the number of soft drink sold if the temperature is
Chapter 1 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