Chapter SH, Problem 8.9.1EP

(a)

To determine

To calculate: To make a scatter plot of the computer sales and draw a line of fit

Answer to Problem 8.9.1EP

The scatter plot is created and line of fit is drawn

Explanation of Solution

Given information: Table showing the amount of sales of computers in U.S

Year	Computer Sales ($ billion)
1990	8.9
1994	18.0
1996	23.6
1998	28.6
2000	35.1

Calculation:

Given the table showing the amount of sales of computer in U.S

Year	Computer Sales ($ billion)
1990	8.9
1994	18.0
1996	23.6
1998	28.6
2000	35.1

On plotting the points on graph and the line of fit is as follows:

  

Conclusion:

Hence, scatter plot is created and line of fit is drawn

(a)

To determine

To calculate: To estimate the computer sales in $2010$

Answer to Problem 8.9.1EP

Computer sales in $2010$ is $60.4$ billion dollars.

Explanation of Solution

Given information: Table showing the amount of sales of computers in U.S

Year	Computer Sales ($ billion)
1990	8.9
1994	18.0
1996	23.6
1998	28.6
2000	35.1

Calculation:

Given the table showing the amount of sales of computer in U.S

Year	Computer Sales ($ billion)
1990	8.9
1994	18.0
1996	23.6
1998	28.6
2000	35.1

On plotting the points on graph and the line of fit is as follows:

  

From the graph,

Sales in $2010$ $=60.4$

Conclusion:

Hence, Computer sales in $2010$ is $60.4$ billion dollars.

(c)

To determine

To calculate: To write the equation in slope-intercept form

Answer to Problem 8.9.1EP

Equation in slope-intercept form is $y=2.65x-5266.1$

Explanation of Solution

Given information: Points on line are $\left(1994,18.0\right)$ and $\left(1998,28.6\right)$

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Equation of line passing through the points given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given the points on line are $\left(1994,18.0\right)$ and $\left(1998,28.6\right)$

Equation of line passing through the points given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Substituting the values,

  $\begin{array}{l}y-18=\frac{28.6-18}{1998-1994}\left(x-1994\right)\\ y-18=\frac{10.6}{4}\left(x-1994\right)\\ y-18=2.65\left(x-1994\right)\\ y-18=2.65x-5284.1\\ y=2.65x-5266.1\end{array}$

Conclusion:

Hence, equation in slope-intercept form is $y=2.65x-5266.1$

(d)

To determine

To calculate: To find the amount of computer sales in $2020$

Answer to Problem 8.9.1EP

The computer sales in $2020$ is $86.9$ billion dollars.

Explanation of Solution

Given information: Points on line are $\left(1994,18.0\right)$ and $\left(1998,28.6\right)$

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Equation of line passing through the points given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given the points on line are $\left(1994,18.0\right)$ and $\left(1998,28.6\right)$

Equation of line passing through the points given as

  $y=2.65x-5266.1$

In order to calculate the computer sales in $2020$ , substitute $x=2020$ in above equation,

  $\begin{array}{l}y=2.65\left(2020\right)-5266.1\\ y=5353-5266.1\\ y=86.9\end{array}$

Conclusion:

Hence, computer sales in $2020$ is $86.9$ billion dollars.