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Question 154153: Single women. The percentage of women in the 20–24 age
group who have never married went from 55% in 1970 to
73% in 2000 (Census Bureau, www.census.gov). Let 1970
be year 0 and 2000 be year 30.
a) Find and interpret the slope of the line through the
points (0, 55) and (30, 73).
b) Find the equation of the line in part (a).
c) What is the meaning of the y-intercept?
d) Use the equation to predict the percentage in 2010.
e) If this trend continues, then in what year will the
percentage of women in the 20–24 age group who have
never married reach 100%?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Single women. The percentage of women in the 20–24 age
group who have never married went from 55% in 1970 to
73% in 2000 (Census Bureau, www.census.gov).
Let 1970 be year 0 and 2000 be year 30.
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a) Find and interpret the slope of the line through the
points (0, 55) and (30, 73).
slope = (73-55)/(30-0) = 0.6
Interpretation: Percentage of women in the 20-24 age group
who have never married increases by 0.6% each year after 1970.
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b) Find the equation of the line in part (a).
Percent(at year x) = 0.6x + 55 for x >= 1970
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c) What is the meaning of the y-intercept?
In 1970 the percent was 55%
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d) Use the equation to predict the percentage in 2010.
P(40) = 0.6*40 + 55 = 55+24 = 79%
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e) If this trend continues, then in what year will the
percentage of women in the 20–24 age group who have
never married reach 100%?
100 = 0.6x + 55
0.6x = 45
x = 75 years after 1970
1970 + 75 = 2045
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Cheers,
Stan H.
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