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

$1360743013505$

$2375845014515$

$3390947015545$

$43751045516560$

$53901147517575$

$64001249518590$

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 $940$ 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.$)$