Chapter 1.3, Problem 88E

a.

To determine

Represent annual sales with the slopes of lines.

Answer to Problem 88E

  $2008-2009$ Sales have least increase $\boxed{4.06}$ .

  $2009-2010$ Sales have greatest increase $\boxed{28.69}$ .

Explanation of Solution

Given information:

The graph shows the sales (in billions of dollars) for Apple Inc. in the years $2004$ through $2010$ .

  

Use the slopes of the line segments to determine the years in which the sales showed the greatest increase and the least increase.

Calculation:

Consider The graph shows the sales (in billions of dollars) for Apple Inc. in the years $2004$ through $2010$ .

  

The slope $m$ of the noncritical line through $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

  $m=\frac{y_2-y_1}{x_2-x_1}$

Now consider each point given in the graph,

Slope between points $\left(4,8.28\right)and\left(5,13.93\right)$

  $\begin{array}{l}m=\frac{13.98-8.28}{5-4}\\ =5.65\end{array}$

Slope between points $\left(5,13.93\right)and\left(6,19.32\right)$

  $\begin{array}{l}m=\frac{19.32-13.93}{6-5}\\ =5.39\end{array}$

Slope between points $\left(6,19.32\right)and\left(7,24.01\right)$

  $\begin{array}{l}m=\frac{24.01-19.32}{7-6}\\ =4.69\end{array}$

Slope between points $\left(7,24.01\right)and\left(8,32.48\right)$

  $\begin{array}{l}m=\frac{32.48-24.01}{8-7}\\ =8.47\end{array}$

Slope between points $\left(8,32.48\right)and\left(9,36.54\right)$

  $\begin{array}{l}m=\frac{36.54-32.48}{9-8}\\ =4.06\end{array}$

Slope between points $\left(9,36.54\right)and\left(10,65.23\right)$

  $\begin{array}{l}m=\frac{65.23-36.54}{10-9}\\ =28.69\end{array}$

Hence for years $2008-2009$ sales has laest increase $\boxed{4.06}$ and for years $2009-2010$

sales has greatest increase $\boxed{28.69}$

b.

To determine

Represent annual sales with the slopes of lines.

Answer to Problem 88E

Slope of line connecting the points for year $2004$ through $2010$ is $\boxed{9.49}$ .

Explanation of Solution

Given information:

The graph shows the sales (in billions of dollars) for Apple Inc. in the years $2004$ through $2010$ .

  

Find the slope of the line segment connecting the points for the years $2004$ and $2010$ .

Calculation:

Consider The graph shows the sales (in billions of dollars) for Apple Inc. in the years $2004$ through $2010$ .

  

The slope $m$ of the noncritical line through $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

  $m=\frac{y_2-y_1}{x_2-x_1}$

Slope of line connecting the points $\left(4,8.28\right)and\left(10,65.23\right)$

  $\begin{array}{l}m=\frac{65.23-8.28}{10-4}\\ =9.49\end{array}$

Hence Slope of line connecting the points for year $2004$ through $2010$ is $\boxed{9.49}$ .

c.

To determine

Represent annual sales with the slopes of lines.

Answer to Problem 88E

The slope in part $\left(b\right)$ shows that increase in sales from $2004$ is $2010$ is $\boxed{9.49}$

Explanation of Solution

Given information:

The graph shows the sales (in billions of dollars) for Apple Inc. in the years $2004$ through $2010$ .

  

Interpret the meaning of the slope in part $\left(b\right)$ in the context of the problem.

Calculation:

The slope in part $\left(b\right)$ shows that increase in sales from $2004$ is $2010$ is $\boxed{9.49}$

Hence the slope in part $\left(b\right)$ shows that increase in sales from $2004$ is $2010$ is $\boxed{9.49}$