PRECALCULUS:...COMMON CORE ED.-W/ACCESS
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
10th Edition
ISBN: 9780134781839
Author: Demana
Publisher: PEARSON
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Chapter P.4, Problem 54E
Solution

a.

The scatter plot of given data.

  PRECALCULUS:...COMMON CORE ED.-W/ACCESS, Chapter P.4, Problem 54E , additional homework tip  1

Given:

The table shows world population in millions,

    Time (Years)U.S. Exports (billions of dollars)
    2005211.9
    2010249.3
    2012292.7
    2013300.8
    2014312.8
    2015280.6

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=y2y1x2x1
  • The slope of a line is defined as rise over run

Calculation:

The scatter plot of the given data is shown below:

  PRECALCULUS:...COMMON CORE ED.-W/ACCESS, Chapter P.4, Problem 54E , additional homework tip  2

b.

The linear equation that gives the U.S Exports y , in terms of the years x using the year 2005 and 2015.

  y=6.87x2005+211.9

Given:

The table shows world population in millions,

    Time (Years)U.S. Exports (billions of dollars)
    2005211.9
    2010249.3
    2012292.7
    2013300.8
    2014312.8
    2015280.6

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=y2y1x2x1
  • 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 0,4453 and 30,6972 as shown below

  m=y2y1x2x1=69724453300=25193084

Now, substitute m=6.87 and x1,y1=2005,211.9 into the point-slope form of the line and simplify further as shown below

  yy1=mxx1y211.9=6.87x2005y=6.87x2005+211.9

Thus, the linear equation for world population is y=6.87x2005+211.9 .

The graph of the equation y=6.87x2005+211.9 is shown on the scatter plot of the data below.

  PRECALCULUS:...COMMON CORE ED.-W/ACCESS, Chapter P.4, Problem 54E , additional homework tip  3

c.

The U.S. export in 2020 using the equation.

  $314.95 billion

Given:

The linear equation for U.S. export is y=6.87x2005+211.9 .

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=y2y1x2x1
  • The slope of a line is defined as rise over run

Calculation:

In order to predict the world population in 2020, draw a vertical line at x=2020 and locate the intersection point with the line as shown below

  y=6.87x2005+211.9y=6.8720202005+211.9y=6.8715+211.9y=314.95

Thus, the U.S. export to Canada in 2020 is $314.95 billion .

Chapter P Solutions

PRECALCULUS:...COMMON CORE ED.-W/ACCESS

Ch. P.1 - Prob. 1ECh. P.1 - Prob. 2ECh. P.1 - Prob. 3ECh. P.1 - Prob. 4ECh. P.1 - Prob. 5ECh. P.1 - Prob. 6ECh. P.1 - Prob. 7ECh. P.1 - Prob. 8ECh. P.1 - Prob. 9ECh. P.1 - Prob. 10ECh. P.1 - Prob. 11ECh. P.1 - Prob. 12ECh. P.1 - Prob. 13ECh. P.1 - Prob. 14ECh. P.1 - Prob. 15ECh. P.1 - Prob. 16ECh. P.1 - Prob. 17ECh. P.1 - Prob. 18ECh. P.1 - Prob. 19ECh. P.1 - Prob. 20ECh. P.1 - Prob. 21ECh. P.1 - Prob. 22ECh. P.1 - Prob. 23ECh. P.1 - Prob. 24ECh. P.1 - Prob. 25ECh. P.1 - Prob. 26ECh. P.1 - Prob. 27ECh. P.1 - Prob. 28ECh. P.1 - Prob. 29ECh. P.1 - Prob. 30ECh. P.1 - Prob. 31ECh. P.1 - Prob. 32ECh. P.1 - Prob. 33ECh. P.1 - Prob. 34ECh. P.1 - Prob. 35ECh. P.1 - Prob. 36ECh. P.1 - Prob. 37ECh. P.1 - Prob. 38ECh. P.1 - Prob. 39ECh. P.1 - Prob. 40ECh. P.1 - Prob. 41ECh. P.1 - Prob. 42ECh. P.1 - Prob. 43ECh. P.1 - Prob. 44ECh. P.1 - Prob. 45ECh. P.1 - Prob. 46ECh. P.1 - Prob. 47ECh. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. 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