A pharmacist has been monitoring sales of a certain over$-$the$-$counter pain reliever. Daily sales during the last $15$ days were

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a$.$ Assume the data refer to demand rather than sales. Using trend$-$adjusted exponential smoothing with an initial forecast of $42$ for Day $8,$ an initial trend estimate of $2,$ and $\backslash ($ a$=\backslash$beta$=\mathrm{.}2\backslash ),$ develop demand forecasts for Days $9$ through $16.$ Then compute the resultant MSE using the error values from Days $8$ through $15.$

Note: Round your intermediate period$-$by$-$period forecast and error values to $3$ decimal places. Round your final MSE answer to $3$ decimal places.

MSE