Chapter 1.1, Problem 87E

a.

To determine

Calculate the years in which the sales showed the great increase and greatest decrease by seeing the slope.

Answer to Problem 87E

The greatest increase is $ $11.431$ billion and the greatest decrease is $ $954$ million .

Explanation of Solution

Given: It is given in the question that the graph shows the sales y (in billions of dollars) of the Coca − cola Company each year x from $2005$ through $2012$ and the graph is shown below:

  

Concept Used:

In this , use the concept of graph analysis that how to read the graph data and by this calculate the question.

Calculation: Firstly , take the each year and calculate the slope and by this we easily get the lowest and the greatest.

YEARS	SLOPE
$2005-2006$	$24.088-23.104=0.984$
$2006-2007$	$28.857-24.088=4.769$
$2007-2008$	$31944-28.857=3.087$
$2008-2009$	$30.990-31.944=-0.954$
$2009-2010$	$35.123-30.990=4.133$
$2010-2011$	$46.554-35.123=11.431$
$2011-2012$	$48.017-46.554=1.463$

So , by seeing the table we find that the greatest increase was $ $11.431$ billion from $2010-2011$ .

The greatest decrease was $ $954$ million from $2008-2009$ .

Conclusion:

The greatest increase is $ $11.431$ billion and the greatest decrease is $ $954$ million .

b.

To determine

Calculate the equation of the line between the years $2005$ and $2012$ .

Answer to Problem 87E

The equation of the line between the years is $y=3.559x+5.309$ .

Explanation of Solution

Given: It is given in the question that the graph shows the sales y (in billions of dollars) of the Coca − cola Company each year x from $2005$ through $2012$ and the graph is shown below:

  

Concept Used:

In this , use the concept of slope formula and point slope form the formula used is $y-y_1=m(x-x_1)$ .

Calculation:

By using the points $(5,23.104)$ and $(12,48.017)$ ,

The slope is $m=\frac{y_2-y_1}{x_2-x_1}=\frac{48.017-23.104}{12-5}=3.559$

Now, using the point slope form to get the equation:

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-23.104=3.559(x-5)\\ y-23.104=3.559x-17.795\\ y=3.559x+5.309\end{array}$

Conclusion:

The equation is $y=3.559x+5.309$ .

c.

To determine

Identify the meaning of the slope of the line grom part (b) in the context of the problem.

Answer to Problem 87E

The slope in the equation means that there was an average increase in sales of about $\$3.559$ billion.

Explanation of Solution

Given: It is given in the question that the graph shows the sales y (in billions of dollars) of the Coca − cola Company each year x from $2005$ through $2012$ and the graph is shown below:

  

Concept Used:

In this, use the concept to read and understand the equation and get the answer from it.

Calculation: The equation that get from part (b) is $y=3.559x+5.309$ .

From the equation it is concluded that there was an average increase in sales of about $\$3.559$ billion from $2005to2012$ .

Conclusion:

It is conclude that the average sales is $\$3.559$ .

d.

To determine

Find the sales of the Coca − cola company in $2017$ by using the equation from part (b).Find whether it is accurate or not,give reason.

Answer to Problem 87E

The approximate sales of the Coca − Cola Company in 2017 is $\$65.812$ .It is not accurate.

Explanation of Solution

Given: It is given in the question that the graph shows the sales y (in billions of dollars) of the Coca − cola Company each year x from $2005$ through $2012$ and the graph is shown below:

  

Concept Used:

In this, use the concept of putting the value in the equation and finding the answer.

Calculation: Here, in part (b) the equation will be $y=3.559x+5.309$ .

Now ,put $x=17$ in the equation to get some approximate value of sales,

  $\begin{array}{l}y=3.559x+5.309\\ y=3.559(17)+5.309\\ y=60.503+5.309\\ y=65.812\end{array}$

It is not the accurate sale as the seasonal changes may affect the sale of the product.

Conclusion:

The approximate sales in 2017 is $\$65.812$ .