The price of gold is used by some financial analysts as a barometer of investors' expectations of inflation, with the price of gold tending to increase as concerns about inflation increase. The table below shows the average annual price of gold (in dollars per ounce) from 1990 through 2015.

a. Compute an exponentially smoothed series for the gold price time series for the period from 1990 to 2015, using a smoothing coefficient of w = .8.
b. Plot the original series and the exponentially smoothed series on the same graph. Comment on the trend observed.

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Year Year Price Price 1990 384 2003 363 2004 1991 1992 1993 1994 1995 362 344 360 384 384 410 445 603 695 872 972 2005 2006 2007 2008 1996 1997 1998 1999 2000 2001 2002 388 331 294 279 279 271 2009 2010 2011 2012 2013 2014 2015 1,225 1,572 1,669 1,411 1,267 1,160 310