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Air Travel: International The following table shows total international travel on U.S. air carriers in specified months from January 2006 to July 2008 ( ( t = 0 ) representsJanuary 2006): t 0 3 6 9 12 15 18 21 24 27 30 Revenue Passenger Miles (billions) 18 19 23 19 19 20 24 20 25 20 25 a. Plot the data, and roughly estimate the period P and the parameters C, A, and β fora cosine model. b. Find the best-fit cosine curve approximating the given data. [You may have to use your estimates from part (a) as initial guesses if you are using Solver.] Plot the given data together with the regression curve. (Round coefficients to three decimal places.) c. Complete the following: Based on the regression model, international travel on U.S. air carriers showed a pattern that repeats itself every ___ months, from a low of ___ to a high of ___ billion revenue passenger miles. (Round answers to the nearest whole number.) [ HINT: See Example 5.]

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Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248

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Chapter
Section
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248
Chapter 9.1, Problem 58E
Textbook Problem
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Air Travel: International The following table shows total international travel on U.S. air carriers in specified months from January 2006 to July 2008 ( ( t = 0 ) representsJanuary 2006):

t 0 3 6 9 12 15 18 21 24 27 30
Revenue Passenger Miles (billions) 18 19 23 19 19 20 24 20 25 20 25

a. Plot the data, and roughly estimate the period P and the parameters C, A, and β fora cosine model.

b. Find the best-fit cosine curve approximating the given data. [You may have to use your estimates from part (a) as initial guesses if you are using Solver.] Plot the given data together with the regression curve. (Round coefficients to three decimal places.)

c. Complete the following: Based on the regression model, international travel on U.S. air carriers showed a pattern that repeats itself every ___ months, from a low of ___ to a high of ___ billion revenue passenger miles. (Round answers to the nearest whole number.) [HINT: See Example 5.]

(a)

To determine

To graph: The data from the table that shows total domestic air travel on U.S. air carries in specified months from January 2006 to July 2008 and (t=0) represents January 2006 using the TI-83 graphing calculator and also roughly estimate the period P and the parameters C, A and β for a cosine model.

t 0 3 6 9 12 15 18 21 24 27 30
Revenue Passenger Miles (billions) 18 19 23 19 19 20 24 20 25 20 25

Explanation of Solution

Given Information:

The total domestic air travel on U.S. air carries in specified months from January 2006 to July 2008 and (t=0) represents January 2006.

t 0 3 6 9 12 15 18 21 24 27 30
Revenue Passenger Miles (billions) 18 19 23 19 19 20 24 20 25 20 25

Graph:

Consider the provided table:

t 0 3 6 9 12 15 18 21 24 27 30
Revenue Passenger Miles (billions) 18 19 23 19 19 20 24 20 25 20 25

Graph of the table data using the Ti-83 graphing calculator as follows:

Step 1: Press “STAT” option and press 1

(b)

To determine

To calculate: The best-fit cosine curve approximating the data of the table that shows total domestic air travel on U.S. air carries in specified months from January 2006 to July 2008 and (t=0) represents January 2006 and also sketch the graph with the regression curve.

t 0 3 6 9 12 15 18 21 24 27 30
Revenue Passenger Miles (billions) 18 19 23 19 19 20 24 20 25 20 25

(c)

To determine

To fill: The blanks in the statement “Based on the regression model, international travel on U.S. air carriers showed a pattern that repeat itself every __________ months, from a low of _______ to a high of __________ billion revenue passengers”.

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Chapter 9 Solutions

Applied Calculus
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Ch. 9.1 - In Exercises 1318, model each curve with a sine...Ch. 9.1 - In Exercises 1318, model each curve with a sine...Ch. 9.1 - In Exercises 1318, model each curve with a sine...Ch. 9.1 - In Exercises 1924, model each curve with a cosine...Ch. 9.1 - In Exercises 1924, model each curve with a cosine...Ch. 9.1 - In Exercises 1924, model each curve with a cosine...Ch. 9.1 - In Exercises 1924, model each curve with a cosine...Ch. 9.1 - In Exercises 1924, model each curve with a cosine...Ch. 9.1 - In Exercises 1924, model each curve with a cosine...Ch. 9.1 - In Exercises 2528, use the conversion formula...Ch. 9.1 - In Exercises 2528, use the conversion formula...Ch. 9.1 - In Exercises 2528, use the conversion formula...Ch. 9.1 - In Exercises 2528, use the conversion formula...Ch. 9.1 - Some Identities Starting with the identity...Ch. 9.1 - Some Identities Starting with the identity...Ch. 9.1 - Exercises 31-38 are based on the addition...Ch. 9.1 - Exercises 31-38 are based on the addition...Ch. 9.1 - 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