Following are the data on demand for white bread loaves at a bakery.

Day Loaves

$1194$

$2214$

$3217$

$4228$

$5237$

$6240$

$7249$

$8259$

$9258$

$10267$

$11281$

$12278$

$13279$

$14288$

$15313$

a$.$ Develop a linear trend equation for the above data on demand for white bread loaves at a bakery $($use of Excel$$s Trendline, with display Equation on chart option, is recommended$),$ and use it to forecast demand on day $16.($Round the final answers to $2$ decimal places.$)$

Y $=$

$7\mathrm{.}08$

x $+$

$196\mathrm{.}84$

Forecast demand on day $16$

$310\mathrm{.}12$

b$.$ The variations around the linear trend line seem to have above$-$ and below$-$the$-$line runs. Therefore, use trend$-$adjusted exponential smoothing with $\backslash$alpha $=0\mathrm{.}3$ and $\backslash$beta $=0\mathrm{.}2$ to model the bread demand. Use the first four days to estimate the smoothed initial trend that you use for periods $4$ and $5($use the increase from day $1$ to day $4$ divided by $3).$ Also, use A$4$ to estimate S$4.$ Start forecasting day $5.$ What is the forecast for day $16?($Round the final answers to $2$ decimal places.$)$

Period TAFt

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

$13$

$14$

$15$

$16$

Forecast for day $16$