Freight car loadings over an $18-$week period at a busy port are as follows:

$\backslash$table$[[$Week$,$Number,Week,Number,Week,Number$],[1,220,7,350,13,460],[2,245,8,360,14,475],[3,280,9,400,15,500],[4,275,10,380,16,510],[5,300,11,420,17,525],[6,310,12,450,18,541]]$

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a$.$ Determine a linear trend line for expected freight car loadings. $($Round your intermediate calculations and final answers to $2$ decimal places.$)$

hat$(Y)=$

b$.$ Use the trend equation to predict expected loadings for weeks $20$ and $21.($Round your final answers to $2$ decimal places.$)$

The forecasted demand for week $20$ and $21$ is

and

respectively.

c$.$ The manager intends to install new equipment when the volume exceeds $800$ loadings per week. Assuming the current trend continues, the loading volume will reach that level in approximately how many more weeks? $($Use the rounded answers, as required, from any previous part of this problem. Do not round any other intermediate calculations. Round your final answer to $2$ decimal places.$)$

It would take approximately

more weeks.