The table shows the numbers $y($in millions$)$ of people ages $16$ and older that were not in the U$.$S$.$ labor force from $2003$ through $2013.$

$\backslash$table$[[$Year$,$Number of People$],[2003,74\mathrm{.}7],[2004,76],[2005,76\mathrm{.}8],[2006,77\mathrm{.}4],[2007,78\mathrm{.}7],[2008,79\mathrm{.}5],[2009,81\mathrm{.}7],[2010,83\mathrm{.}9],[2011,86],[2012,88\mathrm{.}3],[2013,90\mathrm{.}3]]$

a$)$ Use the regression feature of the calculator to determine a linear model for the year since $2000$ and number of people. $($do not round coefficients$).$ Identify the correlation coefficient.

b$)$ Interpret the slope of your linear model in context.

c$)$ Determine a quadratic model for the data. Do not round coefficients.

d$)$ Which is the better fit? How do you know?

$5.$ The revenue of a company is given by $R(x)=x(2000-60x)$ and the cost is given by $c(x)=4000+500x$ where $x$ is number of units sold in millions.

a$)$ What is the price$-$demand function?

b$)$ What are the fixed costs for the company?

c$)$ Write the profit function for this scenario.

$6.$ The average number of persons per household in the U$.$S$.$ has been shrinking steadily for as long as statistics have been kept and is approximately linear with respect to time. In $1980,$ there were about $2\mathrm{.}76$ persons per household, and in $2012$ there were about $2\mathrm{.}55.$ Write a linear equation that gives the number of people per household based on the year. Then use your equation to predict the household size in $2025.$ DO NOT use linear regression.

e$)$ Use your model to predict the number of people over $16$ that were not in the labor force in $2014.$