Problem $3-7($Algo$)$

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

Week Number Week Number Week Number

$1400746513575$

$2415849514580$

$3430952515610$

$44151051016625$

$54301154017640$

$64351257018655$

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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 $980$ 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.$)$