Given the following demand data, use exponential smoothing to forecast the demand in time period $13$:

Time $123456789101112$

Demand $1058211110994991171161039689103$

$($a$)$ Use the average over the $12$ time periods as the initial estimate $($S$0)$

and try different $\backslash$alpha values $($from $0\mathrm{.}1$ to $0\mathrm{.}9$ with an increment of $0\mathrm{.}1).$

Which $\backslash$alpha value gives the best t to the demand data