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CHAPTER 2
Linear Models, Equations, and Inequalities
44. Applying the intersection of graphs method
46. a.
For the first birth, let x1 1970, y1 22.1, and x2 2010, y2 25.5. Then,
y2 y1 25.5 22.1 0.085 x2 x1 2010 1970
y y1 m( x x1 ) y 22.1 0.085( x 1970) y 22.1 0.085 x 167.45
[0, 50] by [–10, 100]
y 0.085 x 145.35
The solution is (18.715,53.362 ) . In 1979, the percent of male students enrolled in college within 12 months of high school graduation equaled the percent of female students enrolled in college within 12 months of high school graduation. 45. yH = 0.224 x + 9.0 (the % of Hispanics)
yB = 0.057 x + 12.3 (the % of blacks)
representing the median age at giving first birth as a function of year.
b.
For the first marriage, let x1 1970, y1 20.9, and x2 2010, y2 26.1. y2 y1 26.1 20.9 0.13 x2 x1 2010 1970
Setting the first equation equal
Then,
to the second equation, solve for x:
y y1 m( x x1 )
0.224 x + 9.0 = 0.057 x + 12.3 .167 x = 3.3
y 20.9 0.13( x 1970) y 20.9 0.13 x 256.1
3.3 x= = 19.76 ≈ 20 .167
y 0.13x 235.2 representing the median age for
Thus, 20 years after 1990, in the year 2010, the percent of Hispanics in the U.S. civilian non-institutional population equaled the percent of blacks.
women at first marriage as a function of year.
c. To determine the crossover point, set the two linear equations found in the two previous parts equal, and solve for x. Thus, 0.085 x 145.35 0.13x 235.2
89.85 0.045 x x 1996.7 1997 No; the approximation is not the same point as when the actual crossover occurred.
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Full file at https://testbankuniv.eu/College-Algebra-in-Context-5th-Edition-Harshbarger-Solutions-Manual