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nexus9112 [7]
3 years ago
8

The idea of a large, stable middle class (defined as those with annual household incomes in 2010 between $42,000 and $126,000 fo

r 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. Research has shown that this decline was 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.
Mathematics
1 answer:
ser-zykov [4K]3 years ago
7 0

Answer:

f(t) = -0.025t + 0.61

In which t is measured in decades.

Step-by-step explanation:

A linear function f(t) has the following format:

f(t) = at + b

We are given two points of the function, so we can solve a system of equations to find the values for a and b.

61% of all adults in 1971 (t = 0)

This means that f(0) = 0.61

So

f(t) = at + b

0.61 = a*(0) + b

b = 0.61

51% in 2011 (t = 4)

This means that f(4) = 0.51

So

f(t) = at + 0.61

0.51 = 4a + 0.61

4a = -0.10

a = -0.025

So the linear function is:

f(t) = -0.025t + 0.61

In which t is measured in decades.

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