Concept explainers
a.
To calculate the total number of bagels sold over the 11-year period.
a.
Answer to Problem 25E
The total number of bagels sold over 11-year period is 797.5 thousand.
Explanation of Solution
Given information:
year | Sales
(thousands) |
1995 | 5 |
1996 | 8.9 |
1997 | 16 |
1998 | 26.3 |
1999 | 39.8 |
2000 | 56.5 |
2001 | 76.4 |
2002 | 99.5 |
2003 | 125.8 |
2004 | 155.3 |
2005 | 188 |
Calculation:
Total no bagels sold
Therefore,
The total number of bagels sold over 11-year period is 797.5 thousand.
b.
To model annual bagel sales (in thousands) as a function of B(x) using quadratic regression, where x is the number of years after 1995.
b.
Answer to Problem 25E
The model for annual bagel sales
Explanation of Solution
Given information:
year | Sales
(thousands) |
1995 | 5 |
1996 | 8.9 |
1997 | 16 |
1998 | 26.3 |
1999 | 39.8 |
2000 | 56.5 |
2001 | 76.4 |
2002 | 99.5 |
2003 | 125.8 |
2004 | 155.3 |
2005 | 188 |
Calculation:
Assume the quadratic regression as
To evaluate a, band c put values of sales after 1 year of 1995
Therefore,
The model for annual bagel sales
c.
To integrate B(x)over the interval [0, 11] to find the bagel sales for 11 years.
c.
Answer to Problem 25E
The bagel sales for 11 year is approximately 904.02 thousands
Explanation of Solution
Given information:
The interval of the integration is [0,11]
Calculation:
Integrate B(x)over the interval [0, 11]
Therefore,
The bagel sales for 11 year is approximately 904.02 thousands
d.
To explain graphically why the answer in part (a) is smaller than the answer in part (c).
d.
Answer to Problem 25E
The answer in (a) corresponds to the area of left-hand rectangles. These rectangles lie under the curve B(x). The answer in (c) corresponds to the area under the curve this area is greater than the area of the rectangles.
Explanation of Solution
Given information:
Answer in part (a) is 797.5 thousands
Answer in part (c) is 904.02 thousands
The graph of the function is
The answer in (a) corresponds to the area of left-hand rectangles. These rectangles lie under the curve B(x). The answer in (c) corresponds to the area under the curve this area is greater than the area of the rectangles.
Chapter 8 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
College Algebra with Modeling & Visualization (5th Edition)
University Calculus: Early Transcendentals (4th Edition)
Elementary Statistics
Intro Stats, Books a la Carte Edition (5th Edition)
Precalculus
Algebra and Trigonometry (6th Edition)
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