N (in millions) of households in the United States from 2000 through 2014 can be approximated by N(x) = −0.023(x − 33.12)2 + 131, 0 ≤ t ≤ 14 where t represents the year, with t = 0 corresponding to 2000. (Source: U.S. Census Bureau)
(a) Describe the transformation of the parent function f(x) = x2. Then use a graphing utility to graph the function over the specified domain.
(b) Find the average rate of change of the function from 2000 to 2014. Interpret your answer in the context of the problem.
(c) Use the model to predict the number of households in the United States in 2022. Does your answer seem reasonable? Explain.