The table below shows the inventory$-$sales ratio for manufacturing and trade for a region over a period of $8$ years. Use the method of simple exponential smoothing to obtain forecasts of the inventory$-$sales ratio over the next $4$ years. Use a smoothing constant of $=0\mathrm{.}9.$ Graph the observed time series and forecasts.

$\backslash$table$[[$Year$,$Ratio$],[1,1\mathrm{.}43],[2,1\mathrm{.}44],[3,1\mathrm{.}51],[4,1\mathrm{.}45],[5,1\mathrm{.}41],[6,1\mathrm{.}42],[7,1\mathrm{.}44],[8,1\mathrm{.}41]]$

Complete the table below.

$\backslash$table$[[,,$Exponentially Smoothed Series$],[$Year$,$Ratio,$)=(0\mathrm{.}9$