Chapter 2.2, Problem 81E

Head of household education. The data in the following table relate the percentage of households headed by someone with a bachelor’s degree or higher to the number of years since 2000.

(Source: www.census.gov/prod/2013pubs/p20-569.pdf.)

Number of Years since 2000	Percentage of Households
0	66.0
1	75.2
3	78.3
7	84.0
9	88.5
10	89.2
11	89.9

a. Use regression (see Section R.6) to fit linear, cubic, and quartic functions $y=f\left(x\right)$ to the data, where x is the number of years since 2000 and y is the percentage of households headed by someone with a bachelor’s degree or higher. Which function $f$ best fits the data?

b. What is the domain of $f$?

c. Does f have any relative extrema? How can you tell?