a.

The linear equation of U.S. imports from Mexico, y , in terms of the year x using the points 2005,170.1 and 2015,296.4 .

y=12.63x−2005+170.1

Given:

The table shows U.S. imports from Mexico, y , in selected years x ,

x 2005 2010 2012 2013 2014 2015
y 170.1 230 277.6 280.6 295.7 296.4

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 2005,170.1 and 2015,296.4 as shown below

m=y2−y1x2−x1=296.4−170.12015−2005=126.310=12.63

Now, substitute m=12.63 and x1,y1=2005,170.1 into the point-slope form of the line and simplify further as shown below

y−y1=mx−x1y−170.1=12.63x−2005y=12.63x−2005+170.1

Thus, the linear equation for U.S. imports from Mexico is y=12.63x−2005+170.1 .

b.

The graph of the function y=12.63x−2005+170.1 on the scatter plot of the given data.

Given:

The table shows U.S. imports from Mexico, y , in selected years x ,

x 2005 2010 2012 2013 2014 2015
y 170.1 230 277.6 280.6 295.7 296.4

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=12.63x−2005+170.1 is shown on the scatter plot of the data below.

c.

The import in 2020 using the equation found in part (a).

$359.55 billion

Given:

The linear equation that gives the U.S. imports from Mexico in year x is y=12.63x−2005+170.1 .

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=12.63x−2005+170.1=12.632020−2005+170.1=12.6315+170.1=189.45+170.1=359.55

Thus, the U.S. imports from Mexico in 2020 is $359.55 billion .

Chapter P.4, Problem 51E

Chapter P.4, Problem 53E

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

Ch. P.1 - Prob. 1QR Ch. P.1 - Prob. 2QR Ch. P.1 - Prob. 3QR Ch. P.1 - Prob. 4QR Ch. P.1 - Prob. 5QR Ch. P.1 - Prob. 6QR Ch. P.1 - Prob. 7QR Ch. P.1 - Prob. 8QR Ch. P.1 - Prob. 9QR Ch. P.1 - Prob. 10QR

Ch. P.1 - Prob. 1E Ch. P.1 - Prob. 2E Ch. P.1 - Prob. 3E Ch. P.1 - Prob. 4E Ch. P.1 - Prob. 5E Ch. P.1 - Prob. 6E Ch. P.1 - Prob. 7E Ch. P.1 - Prob. 8E Ch. P.1 - Prob. 9E Ch. P.1 - Prob. 10E Ch. P.1 - Prob. 11E Ch. P.1 - Prob. 12E Ch. P.1 - Prob. 13E Ch. P.1 - Prob. 14E Ch. P.1 - Prob. 15E Ch. P.1 - Prob. 16E Ch. P.1 - Prob. 17E Ch. P.1 - Prob. 18E Ch. P.1 - Prob. 19E Ch. P.1 - Prob. 20E Ch. P.1 - Prob. 21E Ch. P.1 - Prob. 22E Ch. P.1 - Prob. 23E Ch. P.1 - Prob. 24E Ch. P.1 - Prob. 25E Ch. P.1 - Prob. 26E Ch. P.1 - Prob. 27E Ch. P.1 - Prob. 28E Ch. P.1 - Prob. 29E Ch. P.1 - Prob. 30E Ch. P.1 - Prob. 31E Ch. P.1 - Prob. 32E Ch. P.1 - Prob. 33E Ch. P.1 - Prob. 34E Ch. P.1 - Prob. 35E Ch. P.1 - Prob. 36E Ch. P.1 - Prob. 37E Ch. P.1 - Prob. 38E Ch. P.1 - Prob. 39E Ch. P.1 - Prob. 40E Ch. P.1 - Prob. 41E Ch. P.1 - Prob. 42E Ch. P.1 - Prob. 43E Ch. P.1 - Prob. 44E Ch. P.1 - Prob. 45E Ch. P.1 - Prob. 46E Ch. P.1 - Prob. 47E Ch. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - Prob. 50E Ch. P.1 - Prob. 51E Ch. P.1 - Prob. 52E Ch. P.1 - Prob. 53E Ch. P.1 - Prob. 54E Ch. P.1 - Prob. 55E Ch. P.1 - Prob. 56E Ch. P.1 - Prob. 57E Ch. P.1 - Prob. 58E Ch. P.1 - Prob. 59E Ch. P.1 - Prob. 60E Ch. P.1 - Prob. 61E Ch. P.1 - Prob. 62E Ch. P.1 - Prob. 63E Ch. P.1 - In Exercises 63 and 64, use scientific notation to...Ch. P.1 - Prob. 65E Ch. P.1 - Prob. 66E Ch. P.1 - Prob. 67E Ch. P.1 - Prob. 68E Ch. P.1 - Prob. 69E Ch. P.1 - Prob. 70E Ch. P.1 - Prob. 71E Ch. P.1 - Prob. 72E Ch. P.1 - Prob. 73E Ch. P.1 - Prob. 74E Ch. P.1 - Prob. 75E Ch. P.1 - Prob. 76E Ch. P.2 - Prob. 1QR Ch. P.2 - Prob. 2QR Ch. P.2 - Prob. 3QR Ch. P.2 - Prob. 4QR Ch. P.2 - Prob. 5QR Ch. P.2 - Prob. 6QR Ch. P.2 - Prob. 7QR Ch. P.2 - Prob. 8QR Ch. P.2 - Prob. 9QR Ch. P.2 - Prob. 10QR Ch. P.2 - Prob. 1E Ch. P.2 - Prob. 2E Ch. P.2 - Prob. 3E Ch. P.2 - Prob. 4E Ch. P.2 - Prob. 5E Ch. P.2 - Prob. 6E Ch. P.2 - Prob. 7E Ch. P.2 - Prob. 8E Ch. 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