The idea of a large, stable middle class (defined as those with annual household incomes in 2010 between $42,000 and $126,000 for a family of three), is central to America's sense of itself. But the U.S. middle class shrank steadily from 61% of all adults in 1971 (t = 0) to 51% in 2011 (t = 4),

Question

The idea of a large, stable middle class (defined as those with annual household incomes in 2010 between $42,000 and $126,000 for a family of three), is central to America's sense of itself. But the U.S. middle class shrank steadily from 61% of all adults in 1971 (t = 0) to 51% in 2011 (t = 4),
where t is measured in decades.

(a) Find a linear function f(t) giving the percentage of middle-income adults in decade t, where t = 0 corresponds to 1971.

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

oobleck · Answer

so it shrank 10% in 4 decades, or 2.5% per decade, assuming a linear rate of decline. f(t) = 61 - 2.5t