Chapter 16.1, Problem 57E

(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 $\left(t=0\right)$ represents January $2006$ using the $\text{TI-}83$ graphing calculator and also roughly estimate the period P and the parameters C, A and $\beta$ for a cosine model.

t	$0$	$3$	$6$	$9$	$12$	$15$	$18$	$21$	$24$	$27$	$30$
Revenue Passenger Miles (billions)	$43$	$49$	$55$	$47$	$44$	$50$	$57$	$49$	$45$	$48$	$55$

(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 $\left(t=0\right)$ 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)	$43$	$49$	$55$	$47$	$44$	$50$	$57$	$49$	$45$	$48$	$55$

(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 passenger”.