Many of the following problems can be modeled with a linear equation. Analyze them and identify what quantities the variables x and y represent. The information provided in the problems is adequate to determine a point and a slope or two points on the line.
The U.S. Census Bureau reports a wide variety of population information. One bit of information is the percent of the population who never marries.
(a) In 2000, the percent of males in the 25–29 age group who had never married was 51.7%. In 2010 the percent rose to 62.2%.
(i) Based on this information, find the percent of unmarried males as a linear function of time since 2000 in years.
(ii) Use the linear function you found to estimate the percent of males, ages 25–29, who had never married for the year 2008.
(iii) The actual percent given by the Census Bureau for 2008 was 57.6%. How does this compare with your estimate? Does the linear function found in (i) seem to be a reasonably good representation of the growth of the percent?
(b) In 2000, 38.9% of the female population in the 25–29 age range had never married. The percent rose to 47.8% in 2010.
(i) Based on this information, find the percent of females who had never married as a linear function of time since 2000 in years.
(ii) Use the linear function just found to estimate the percent of females, ages 25–29, who had never married for the year 2008.
(iii) The actual percent reported by the Census Bureau for 2008 was 43.4%. Compare the estimate obtained in part (ii). Does the linear function seem to provide a reasonable estimate of the growth of the percent of females who never married?
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