Question

6.9.5-GC Question Help The data in the table below represent the number of dairy farms (in thousands) and the amount of milk produced in billions of pounds) in a country for various years. Complete parts (a) through (d) (a) Using a graphing utility, build a logarithmic model from the data with the number of dairy farms as the independent variable. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals rounded to four decimal places as needed Year Inx Dairy Farms Milk Produced (thousands) (billion pounds) 334 129 266 141 192 146 141 154 165 O A. y= OB. y = + - 1980 1985 1990 1995 2000 2005 2010 Inx 504 177 192

Answer 1

MATHEMATICA

Clear[x] x1 = {334, 266, 192, 141, 104, 75, 62} {334, 266, 192, 141, 104, 75, 62} y = {129, 141, 146, 154, 165, 177, 192} {129, 141, 146, 154, 165, 177, 192} xlog = N[Log(x1]] {5.81114, 5.5835, 5.2575, 4.94876, 4.64439, 4.31749, 4.12713} data = Table[{xlog[[a]], y[[a]]}, {a, 1, 7}] {{5.81114, 129}, {5.5835, 141}, {5.2575, 146}, {4.94876, 154}, {4.64439, 165}, {4.31749, 177}, {4.12713, 192}} LinearModelFit[data, x, x] FittedModel 325.562 – 33.8695 x Answer: y = 325.562 – 33.8695 log(x)

pl - Plot[325.56151846773395 - 33.86952477083684 * Log[x], {x, 60, 340}] 150 200 250 300

p2 = ListPlot [Table [xl[ [a] ], y[ [a]]},{a, 1, 7}]] للللللللللللللللللللللللللللللللله 100 150 200 250 300

Show[p1, p2] 150 200 250 300