Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are shown for the past $12$ weeks:

$\backslash$table$[[$Week$,1,2,3,4,5,6,7,8,9,10,11,12],[\backslash$table$[[$Actual Passenger Miles $($in$],[$thousands$)]],17,20,19,22,20,18,22,20,23,22,15,25]]$

a$)$ Assuming an initial forecast for week $1$ of $17,000$ miles, use exponential smoothing to compute miles for weeks $2$ through $12.$ Use $=0\mathrm{.}18($round your responses to two decimal places$).$

$\backslash$table$[[$Week$,1,2,3,4,5,6,7,8,9,10,11,12],[\backslash$table$[[$Forecasted Passenger$],[$Miles $($in thousands$)]],17\mathrm{.}00,17\mathrm{.}00,17\mathrm{.}54,17\mathrm{.}80,18\mathrm{.}56,18\mathrm{.}82,18\mathrm{.}67,19\mathrm{.}27,19\mathrm{.}40,20\mathrm{.}05,,]]$