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Average Monthly Temperature, F Month, x January, 1 36.0 February, 2 39.0 March, 3 46.8 April, 4 56.8 May, 5 66.0 June, 6 75.2 July, 7 79.8 August, 8 78.1 September, 9 71.0 October, 10 59.5 November, 11 49.6 December, 12 39.7 Source: U.S. National Oceanic and Atmospheric Administration

Average Monthly Temperature, F Month, x January, 1 36.0 February, 2 39.0 March, 3 46.8 April, 4 56.8 May, 5 66.0 June, 6 75.2 July, 7 79.8 August, 8 78.1 September, 9 71.0 October, 10 59.5 November, 11 49.6 December, 12 39.7 Source: U.S. National Oceanic and Atmospheric Administration

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Average Monthly Temperature Data** This table shows the average monthly temperatures in degrees Fahrenheit, collected by the U.S. National Oceanic and Atmospheric Administration. | Month, x | Average Monthly Temperature, °F | |-----------|----------------------------------| | January, 1 | 36.0 | | February, 2 | 39.0 | | March, 3 | 46.8 | | April, 4 | 56.8 | | May, 5 | 66.0 | | June, 6 | 75.2 | | July, 7 | 79.8 | | August, 8 | 78.1 | | September, 9 | 71.0 | | October, 10 | 59.5 | | November, 11 | 49.6 | | December, 12 | 39.7 | **Source:** U.S. National Oceanic and Atmospheric Administration **Explanation:** The data illustrates the change in average temperatures throughout the year, starting from January to December. The temperatures range from a low of 36.0°F in January to a high of 79.8°F in July. This data can be used to study seasonal variations in temperature and understand climatic patterns.
Transcribed Image Text:**Average Monthly Temperature Data** This table shows the average monthly temperatures in degrees Fahrenheit, collected by the U.S. National Oceanic and Atmospheric Administration. | Month, x | Average Monthly Temperature, °F | |-----------|----------------------------------| | January, 1 | 36.0 | | February, 2 | 39.0 | | March, 3 | 46.8 | | April, 4 | 56.8 | | May, 5 | 66.0 | | June, 6 | 75.2 | | July, 7 | 79.8 | | August, 8 | 78.1 | | September, 9 | 71.0 | | October, 10 | 59.5 | | November, 11 | 49.6 | | December, 12 | 39.7 | **Source:** U.S. National Oceanic and Atmospheric Administration **Explanation:** The data illustrates the change in average temperatures throughout the year, starting from January to December. The temperatures range from a low of 36.0°F in January to a high of 79.8°F in July. This data can be used to study seasonal variations in temperature and understand climatic patterns.
**Monthly Temperature** The data below represent the average monthly temperatures for Washington, D.C. (a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form \( y = A \sin (\omega x - \phi) + B \) that models the data. (c) Draw the sinusoidal function found in part (b) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data. --- **Instructions for Educators:** - Begin by introducing the concept of sinusoidal functions and how they can be used to model periodic data. - Use the steps to guide students through creating a scatter plot and fitting a sinusoidal function to given temperature data. - Encourage the use of graphing utilities or software for accurate plotting and analysis. - Discuss the significance of parameters \(A\), \(\omega\), \(\phi\), and \(B\) in shaping the graph of the sinusoidal function. - Engage students in discussions about the accuracy and application of sinusoidal models in real-world scenarios.
Transcribed Image Text:**Monthly Temperature** The data below represent the average monthly temperatures for Washington, D.C. (a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form \( y = A \sin (\omega x - \phi) + B \) that models the data. (c) Draw the sinusoidal function found in part (b) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data. --- **Instructions for Educators:** - Begin by introducing the concept of sinusoidal functions and how they can be used to model periodic data. - Use the steps to guide students through creating a scatter plot and fitting a sinusoidal function to given temperature data. - Encourage the use of graphing utilities or software for accurate plotting and analysis. - Discuss the significance of parameters \(A\), \(\omega\), \(\phi\), and \(B\) in shaping the graph of the sinusoidal function. - Engage students in discussions about the accuracy and application of sinusoidal models in real-world scenarios.
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