Chapter 1.3, Problem 33E

Erosion of the Middle Class 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 $\left(t=0\right)$ to 51% in 2011 $\left(t=4\right)$, where $t$ is measured in decades. Research has shown that this decline was approximately linear.

a. Find a linear function $f\left(t\right)$ 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?