b) For a very small number x, ln (1 + x) x. Therefore, if gt is small then In (1+ gt) gt and, gt = GDPt GDPt_1 1 In ( gt GDPt GDPt1 In Y ln Yt1 gt t Where Y+ is the GDP for the GDP for the given year and Yt-1 is the GDP of the previous year. Now, calculate growth rate approximation using the formula (In Yt In Yt-1) x 100 and check how accurate it is by finding error in actual growth rate and approximated growth rate. Year (t) Per Capita Real GDP (Y+) Per Capita Growth Rate (gt) Approximated Growth Rate (In Y, - In Y)x100 Error 1950 1960 14,339 17,351 1970 23,790 1980 30,732 1990 35,868 2000 43,288 2010 46,406 2011 47,554 2.47 2.44 0.03 2012 47,741 0.3932 0.3924 0.0008 2013 48,066 0.68 0.67 0.01 2014 48,780 1.48 1.47 0.01