Please show all work and answers!

Q38. (18.31). The US trade deficit with Canada (billions of dollars) from 2000 through 2007 is reported as shown in the table. Using exponential smoothing and the smoothing coefficient a = 0.7, what deficit would have been forecast for 2008? Year Actual Deficit Forecast 1 (2000) 51.9 2 (2001) 52.8 3 (2002) 48.2 4 (2003) 51.7 5 (2004) 66.5 6 (2005) 78.5 7 (2006) 71.8 8_(2007) 68.2 [Hint = 72.3126] 9_(2008) [ Hint 1: In order to be able to predict for 2008 one must first obtain the forecast for 2007, which in turn requires a forecast for 2006, etc. So one has to first fill in lines 1-8 for the actual and forecast values. ! [Hint 2: The forecast equation can be simplified to appear as: Next period forecast = 0.7 this period actual + 0.3 this period forecast. I (a) What is the forecast value for 2000? [ Hint: no calculation required.] (b) What is the forecast values for years 2000-2007. (c) What then is the forecast value for 2008