Data collected on the yearly registrations for a Six Sigma seminar at the Quality College are shown in the following table:

$\backslash$table$[[$Year$,1,2,3,4,5,6,7,8,9,10,11],[$Registrations $(000),5\mathrm{.}00,6\mathrm{.}00,5\mathrm{.}00,6\mathrm{.}00,9\mathrm{.}00,9\mathrm{.}00,6\mathrm{.}00,11\mathrm{.}00,13\mathrm{.}00,14\mathrm{.}00,15\mathrm{.}00]]$

a$)$ Calculate the forecasted registrations for years $2$ through $12$ using exponential smoothing, with a smoothing constant $()$ of $0\mathrm{.}40$ and a starting forecast of $6\mathrm{.}00$ for year $1($round your responses to one decimal place$)$:

$\backslash$table$[[$Year$,1,2,3,4,5,6,7,8,9,10,11,12],[$Forecast $(000),6\mathrm{.}00,,,,,,,,,,,$