Tarheels R$$ Us would also like to explore a more sophisticated forecasting method. They want you to

consider exponential smoothing.

a$.$ If you were to use simple exponential smoothing with $\backslash$alpha values of $0\mathrm{.}3,$ what formula would you use

to compute the forecast for the sales of Tarheels R$$ Us t$-$shirts for weeks $2$ to $18?$ Assume the

forecast for week $1$ is equal to the actual sales in week $1.$

b$.$ What impact does increasing or decreasing $\backslash$alpha have?

c$.$ Compute and plot the forecasts for weeks $2-18$ with $\backslash$alpha $=0\mathrm{.}3$ and $\backslash$alpha $=0\mathrm{.}3$Which $\backslash$alpha value seems to be

most appropriate and explain why.