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

Week Number Week Number Week Number

$1290733513490$

$2300837514495$

$3310941515515$

$43001040516525$

$53101144517535$

$63151248518545$

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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.$)$

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

c$.$ The manager intends to install new equipment when the volume exceeds $870$ loadings per week. Assuming the current trend continues, in which week $($at the earliest$)$ should the loading volume reach that level? $($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.$)$