Suppose you want to forecast the number of students who will sign up for a class that you are offering. You have selected an exponential smoothing model with level and trend. Assume that Alpha=0.25, Beta=0.5. The actual demand in each time period t, noted as x(t), and the forecast for year t+1 made at time t, noted as x^(t,t+1), are shown below for the previous five years.  Recall that the carat symbol "^" indicates an estimate or forecasted value.

For example, the forecast for 2012 made in 2011 is 45.5 while the forecast for 2013 made in 2012 is 49.4.

[table][tr][td]Year[/td][td]x(t)[/td][td]x^(t,t+1)[/td][/tr][tr][td]2009[/td][td]40[/td][td]41[/td][/tr][tr][td]2010[/td][td]41[/td][td]43[/td][/tr][tr][td]2011[/td][td]44[/td][td]45.5[/td][/tr][tr][td]2012[/td][td]50[/td][td]49.4[/td][/tr][tr][td]2013[/td][td]57[/td][td][/td][/tr][/table]