Annual limousine production for the selected years is given in the table below.

$($A$)$ Let $x$ represent time $($in years$)$ since $1980,$ and let y represent the corresponding production of limousines$.$ Enter the data in a graphing calculator and find a cubic regression equation for the data.

$($B$)$ Let $L(x)$ denote the regression equation found in part $($A$)$ with coefficients rounded to the nearest hundredth. Find $L(11)$ and $L^{\text{'}}(11).$

$($C$)$ Interpret $L(19)$ and $L^{\text{'}}(19)$ in this context.

$\backslash$table$[[$Year$,\backslash$table$[[$Limousines$],[$Produced$]]],[1980,2500],[1985,6000],[1990,3900],[1995,3400],[2000,6200]]$

$($A$)L(x)=5$

$($Use integers or decimals rounded to the nearest hundredth for any numbers in the equation.$)$