The idea of a large, stable middle class (defined as those with annual household incomes in 2010 between $39,000 and $118,000 for a family of three), is central to America's sense of itself.

Question

The idea of a large, stable middle class (defined as those with annual household incomes in 2010 between $39,000 and $118,000 for a family of three), is central to America's sense of itself. But the U.S. middle class has been shrinking steadily from 61% of all adults in 1971 (t = 0)

 to 51% in 2011 (t = 4),

 where t is measured in decades. Research has shown that this decline is approximately linear.†(a) Find a linear function f(t) giving the percentage of middle-income adults in decade t, where t = 0

 corresponds to 1971.

f(t) = 

 

(b) If this trend continues, what will the percentage of middle-income adults be in 2021?

 %

Answer 1

The slope is (61-51)/4 = 10/4 = 5/2

(0,61) is the y-intercept, so:

y = 61 - (5/2)t

for 2021, t=5

so y = 61 - (5/2)*5

= 61 - 25/2

= (122-25)/2

= 97/2

= 48.5%