The table gives the cumulative sales of iPods since their introduction.

Cumulative iPod Sales

$\backslash$table$[[$Year$,\backslash$table$[[$Sales$],[($million iPods$)]]],[2003,2\mathrm{.}82],[2004,4\mathrm{.}836],[2005,29\mathrm{.}933],[2006,68\mathrm{.}942],[2007,118\mathrm{.}372],[2008,173\mathrm{.}4]]$

$($a$)$ Find the function for the quadratic model that gives sales in million iPods, where $x$ is the number of years after $2003,$ with data from $0x5.($Round all numerical values to three decimal places.$)$

$s(x)=$ million iPods

$($b$)$ Write the derivative for the sales model. $($Round all numerical values to three decimal places.$)$

$s^{\text{'}}(x)=$ million iPods per year

$($c$)$ Calculate the rate of change of cumulative sales in $2006.($Round your answer to three decimal places.$)$ million iPods per year

Interpret the rate of change of cumulative sales in $2006.($Round your answer to three decimal places.$)$

In $2006,$ cumulative iPod sales were $$ by $$ million per year.