PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.4, Problem 51E
Solution

a.

The linear equation of Americans’ spending y in terms of the year x using the points 1990,3.8 and 2010,10.2 .

  y=0.32x−1990+3.8

Given:

The table shows expenses y in selected years x ,

    x 199019952000200520102015
    y 3.85.06.88.810.212.3

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

In order to find the linear equation, first find the slope of the line using the points 1990,3.8 and 2010,10.2 as shown below

  m=y2−y1x2−x1=10.2−3.82010−1990=6.420=0.32

Now, substitute m=0.32 and x1,y1=1990,3.8 into the point-slope form of the line and simplify further as shown below

  y−y1=mx−x1y−3.8=0.32x−1990y=0.32x−1990+3.8

Thus, the linear equation for Americans’ spending is y=0.32x−1990+3.8 .

b.

The Americans’ expenditures in 2005 using the equation found in part (a).

  $8.6 trillion

Given:

The linear equation that gives the Americans’ expenditure in year x is y=0.32x−1990+3.8 .

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

In order to find the Americans’ expenditure in 2005, substitute x=2005 into the given equation and simplify further as shown below

  y=0.32x−1990+3.8=0.322005−1990+3.8=0.3215+3.8=4.8+3.8=8.6

Thus, the Americans’ expenditure in 2005 is $8.6 trillion .

c.

The Americans’ expenditures in 2020 using the equation found in part (a).

  $13.4 trillion

Given:

The linear equation that gives the Americans’ expenditure in year x is y=0.32x−1990+3.8 .

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

In order to find the Americans’ expenditure in 2020, substitute x=2020 into the given equation and simplify further as shown below

  y=0.32x−1990+3.8=0.322020−1990+3.8=0.3230+3.8=9.6+3.8=13.4

Thus, the Americans’ expenditure in 2020 is $13.4 trillion .

d.

The graph of the function y=0.32x−1990+3.8 on the scatter plot of the given data.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 51E , additional homework tip 1

Given:

The table shows expenses y in selected years x ,

    x 199019952000200520102015
    y 3.85.06.88.810.212.3

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

The graph of the equation y=0.32x−1990+3.8 is shown on the scatter plot of the data below.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 51E , additional homework tip 2

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Chapter P.4, Problem 50E
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Chapter P.4, Problem 52E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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