Chapter 1.4, Problem 66E

Median Sale Price The median sale price p (in thousands of dollars) of an existing one-family home in the United States from 2002 through 2014 (see figure) can be approximated by the model

$p(t)=\{\begin{array}{c}-0.757t^2+20.80t+127.2,2\le t\le 6\\ \begin{array}{l}3.879t^2-82.50t+605.8,\text{ 7}\le t\le \text{11}\\ -4.171t^2+124.34t-714.2,\text{ 12}\le t\le \text{14}\end{array}\end{array}$

where t represents the year, with $t=2$ corresponding to 2002. Use this model to find the median sale price of an existing one-family home in each year from 2002 through 2014. (Source: National Association of Realtors)