Chapter 2.2, 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

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

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 $2014$.