Chapter 1.3, Problem 88E

(a)

To determine

The years in which the sales showed the greatest increase and the least increase.

Answer to Problem 88E

There is the great increase in 2014-2015 and the least increase in 2013-2014.

Explanation of Solution

Given information:

The graph shows the sales in billions of dollars for apple in the year 2009 through 2015.

Formula used:

  $\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

To determine the year in which the sales showed the greatest increase and the least increase. Find the slope of the line segment connecting the points for the years 2009 and 2015.

Use the formula of the slope of a line passing through these two points and make a table.

$\left(x_1,y_1\right)$	$\left(x_2,y_2\right)$	$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$
$\left(9,42.91\right)$	$\left(10,65.23\right)$	$\frac{65.23-42.91}{10-9}=22.32$
$\left(10,65.23\right)$	$\left(11,108.25\right)$	$\frac{108.25-65.23}{11-10}=43.02$
$\left(11,108.25\right)$	$\left(12,156.51\right)$	$\frac{156.51-108.25}{12-11}=48.26$
$\left(12,156.51\right)$	$\left(13,170.91\right)$	$\frac{170.91-156.51}{13-12}=14.4$
$\left(13,170.91\right)$	$\left(14,182.80\right)$	$\frac{182.80-170.91}{14-13}=11.89$
$\left(14,182.80\right)$	$\left(15,233.72\right)$	$\frac{233.72-182.80}{15-14}=50.92$

With the help of above table, the greatest increase is in 2014-2015 and the least increase in 2013-2014.

Conclusion:

There is the great increase in 2014-2015 and the least increase in 2013-2014.

(b)

To determine

The slope of the line segment connecting the point for the years 2009 and 2015.

Answer to Problem 88E

The slope of the line segment is 31.81 which is connecting the points for the years 2009 and 2015.

Explanation of Solution

Given information:

The graph shows the sales in billions of dollars for apple in the year 2009 through 2015.

Formula used:

  $\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Use the formula of the slope of a line passing through $\left(9,42.91\right)$ and $\left(15,233.72\right)$

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{233.72-42.91}{15-9}\\ m=\frac{190.81}{6}\\ m=31.81\end{array}$

Thus, the slope of the line segment is 31.81 which is connecting the points for the years 2009 and 2015.

Conclusion:

The slope of the line segment is 31.81 which is connecting the points for the years 2009 and 2015.

(c)

To determine

meaning of the slope in the context of the problem.

Answer to Problem 88E

The sales increase at the average rate of 31.81 billion dollar per year.

Explanation of Solution

Given information:

The graph shows the sales in billions of dollars for apple in the year 2009 through 2015.

Formula used:

  $\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

The sales increase at the average rate of 31.81 billion dollar per year.

Conclusion:

The sales increase at the average rate of 31.81 billion dollar per year.