a$)$ Initialize the exponential smoothing with correction for trend model using the

above data. Suppose $x_1=145$ and $x_2=160.$ Apply the model through periods

$1$ and $2$ using ${}_{HW}=0\mathrm{.}2$ and ${}_{HW}=0\mathrm{.}3.$ Calculate one$-$period$-$ahead$-$forecast

errors for periods $1$ and $2$ and using these two forecast errors, calculate the

estimate of the standard deviation of one$-$period$-$ahead forecast error,

${}_1=\sqrt[\phantom{2}]{\text{M}\text{S}\text{E}}=\sqrt[\phantom{2}]{\frac{{\displaystyle \underset{?}{\overset{?}{}}}{e}_i^2}{n}}.$ What are your forecast demands for periods $3$ to $8$ as of

end of period $2?$ Round your forecasts to whole numbers.