The intensity of a dougnut-shaped (in cross-section) laser beam was mea- sured. The data had the background noise subtracted, was smoothed, and left and right side data (which should be identical) was averaged, giving the intensity as a function of radius: 160 140 120 100 The xy data is: x = [ 0 0.1341 0.2693 0.4034 0.5386 0.6727 . 0.8079 0.9421 1.0767 1.2114 1.3460 1.4801 ... 1.6153 1.7495 1.8847 2.0199 2.1540 2.2886 .. 2.4233 2.5579 2.6921 2.8273 2.9614 3.0966 .. 3.2307 3.3659 3.5000 ]; y = [ 0 0.0310 0.1588 0.3767 0.6452 0.8780 .. 0.9719 1.0000 0.9918 0.9329 0.8198 0.7707 ... 0.8024 0.7674 0.6876 0.5937 0.5778 0.4755 ... 0.3990 0.3733 0.2870 0.2156 0.2239 0.1314 .. 0.1180 0.0707 0.0259 ]; Note that the data has been re-scaled for the graph shown; your graph will have different values but should have the same shape. Provide a simple approximation to this data. The one obtained in the actual real-life case is shown below; this was a piece-wise polynomial approxi- mation. You can use either equation (1.1) or trial-and-error and your own judgment to find the best order of polynomial to use. 30 f'(x) f()=f(x 5) (equation (10) The intensity of a dougnut-shaped (in cross-section) laser beam was mea- sured. The data had the background noise subtracted, was smoothed, and left and right side data (which should be identical) was averaged, giving the intensity as a function of radius: 160 140 25 The xy data is: x = [ 0 0.1341 0.2693 0.4034 0.5386 0.6727 ... 0.8079 0.9421 1.0767 1.2114 1.3460 1.4801 ... 1.6153 1.7495 1.8847 2.0199 2.1540 2.2886 .. 2.4233 2.5579 2.6921 2.8273 2.9614 3.0966 3.2307 3.3659 3.5000 ]; y = [ 0 0.0310 0.1588 0.3767 0.6452 0.8780 ... 0.9719 1.0000 0.9918 0.9329 0.8198 0.7707 ... 0.8024 0.7674 0.6876 0.5937 0.5778 0.4755 ... 0.3990 0.3733 0.2870 0.2156 0.2239 0.1314 ... 0.1180 0.0707 0.0259 ]; Note that the data has been re-scaled for the graph shown; your graph will have different values but should have the same shape. Provide a simple approximation to this data. The one obtained in the actual real-life case is shown below; this was a piece-wise polynomial approxi- mation. You can use either equation (1.1) or trial-and-error and your own judgment to find the best order of polynomial to use. -200 5 10 15 20 25 30 The intensity of a dougnut-shaped (in cross-section) laser beam was mea- sured. The data had the background noise subtracted, was smoothed, and left and right side data (which should be identical) was averaged, giving the intensity as a function of radius: 160 140 120 100 The xy data is: x = [ 0 0.1341 0.2693 0.4034 0.5386 0.6727 . 0.8079 0.9421 1.0767 1.2114 1.3460 1.4801 ... 1.6153 1.7495 1.8847 2.0199 2.1540 2.2886 .. 2.4233 2.5579 2.6921 2.8273 2.9614 3.0966 .. 3.2307 3.3659 3.5000 ]; y = [ 0 0.0310 0.1588 0.3767 0.6452 0.8780 .. 0.9719 1.0000 0.9918 0.9329 0.8198 0.7707 ... 0.8024 0.7674 0.6876 0.5937 0.5778 0.4755 ... 0.3990 0.3733 0.2870 0.2156 0.2239 0.1314 .. 0.1180 0.0707 0.0259 ]; Note that the data has been re-scaled for the graph shown; your graph will have different values but should have the same shape. Provide a simple approximation to this data. The one obtained in the actual real-life case is shown below; this was a piece-wise polynomial approxi- mation. You can use either equation (1.1) or trial-and-error and your own judgment to find the best order of polynomial to use. 30 f'(x) f()=f(x 5) (equation (10) The intensity of a dougnut-shaped (in cross-section) laser beam was mea- sured. The data had the background noise subtracted, was smoothed, and left and right side data (which should be identical) was averaged, giving the intensity as a function of radius: 160 140 25 The xy data is: x = [ 0 0.1341 0.2693 0.4034 0.5386 0.6727 ... 0.8079 0.9421 1.0767 1.2114 1.3460 1.4801 ... 1.6153 1.7495 1.8847 2.0199 2.1540 2.2886 .. 2.4233 2.5579 2.6921 2.8273 2.9614 3.0966 3.2307 3.3659 3.5000 ]; y = [ 0 0.0310 0.1588 0.3767 0.6452 0.8780 ... 0.9719 1.0000 0.9918 0.9329 0.8198 0.7707 ... 0.8024 0.7674 0.6876 0.5937 0.5778 0.4755 ... 0.3990 0.3733 0.2870 0.2156 0.2239 0.1314 ... 0.1180 0.0707 0.0259 ]; Note that the data has been re-scaled for the graph shown; your graph will have different values but should have the same shape. Provide a simple approximation to this data. The one obtained in the actual real-life case is shown below; this was a piece-wise polynomial approxi- mation. You can use either equation (1.1) or trial-and-error and your own judgment to find the best order of polynomial to use. -200 5 10 15 20 25 30