According to the US Census Bureau, \"United States Census 2010\", 33 million Ame

Question

According to the US Census Bureau, "United States Census 2010", 33 million Americans were age 65 or older in 1995; an amount which climbed to 40 million in 2010.

(a) Which of the following linear equations could be used to predict number of Americans age 65 or older (in millions) “y” in a given year “x”, where x = 0 represents the year 1995? Explain/show work.

A. y = 15/7x + 33

B. y = 15/7x + 1995

C. y = 7/15x + 1995

D/ y = 7/15x + 33

(b) Use the equation from part (a) to predict the number of Americans age 65 or older (in millions) in the year 2031. Round answer to nearest tenth of a million people. Show work.

(c) Fill in the blanks to interpret the slope of the equation: The rate of change of number of Americans age 65 or older with respect to time is
______________________ per ________________. (Include units of measurement.)

Explanation / Answer

a This is a linear regression equation where y is the dependen variable and x is the independent variable The 7/15 is the slope of the line and 33 is the constant y intercept The equation of the line is y = 7/15x + 33 Answer D As every year the population is increasing by factor of 7/15 b For year 2031 we have 2031 - 1995 = 36 years so we have y = (7/15*36) + 33 49.8 million c The rate of change of number of Americans age 65 or older with respect to time is (7/15) per year i.e the population is increasing 7/15 million per year i.e 0.4667 millions per year

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