non linear equation with unknown parameters (optimization)

function f=trail6(x)

syms k n a

T=[940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573 940 915 909 898 895 888 879 873 854 851 848 840 823 798 791 773 758 748 731 727 723 706 700 698 673 659 648 623 598 597 587 583 573]

t=[1150,1200,1212,1234,1240,1254,1272,1284,1322,1328,1334,1350,1384,1434,1448,1484,1514,1534,1568,1576,1584,1618,1630,1634,1684,1712,1734,1784,1834,1836,1856,1864,1884,575,600,606,617,620,627,636,642,661,664,667,675,692,717,724,742,757,767,784,788,792,809,815,817,842,856,867,892,917,918,928,932,942,191.700000000000,200,202,205.700000000000,206.700000000000,209,212,214,220.300000000000,221.300000000000,222.300000000000,225,230.700000000000,239,241.300000000000,247.300000000000,252.300000000000,255.700000000000,261.300000000000,262.700000000000,264,269.700000000000,271.700000000000,272.300000000000,280.700000000000,285.300000000000,289,297.300000000000,305.700000000000,306,309.300000000000,310.700000000000,314,115,120,121.200000000000,123.400000000000,124,125.400000000000,127.200000000000,128.400000000000,132.200000000000,132.800000000000,133.400000000000,135,138.400000000000,143.400000000000,144.800000000000,148.400000000000,151.400000000000,153.400000000000,156.800000000000,157.600000000000,158.400000000000,161.800000000000,163,163.400000000000,168.400000000000,171.200000000000,173.400000000000,178.400000000000,183.400000000000,183.600000000000,185.600000000000,186.400000000000,188.400000000000,82.1428571400000,85.7142857100000,86.5714285700000,88.1428571400000,88.5714285700000,89.5714285700000,90.8571428600000,91.7142857100000,94.4285714300000,94.8571428600000,95.2857142900000,96.4285714300000,98.8571428600000,102.428571400000,103.428571400000,106,108.142857100000,109.571428600000,112,112.571428600000,113.142857100000,115.571428600000,116.428571400000,116.714285700000,120.285714300000,122.285714300000,123.857142900000,127.428571400000,131,131.142857100000,132.571428600000,133.142857100000,134.571428600000,57.5000000000000,60,60.6000000000000,61.7000000000000,62,62.7000000000000,63.6000000000000,64.2000000000000,66.1000000000000,66.4000000000000,66.7000000000000,67.5000000000000,69.2000000000000,71.7000000000000,72.4000000000000,74.2000000000000,75.7000000000000,76.7000000000000,78.4000000000000,78.8000000000000,79.2000000000000,80.9000000000000,81.5000000000000,81.7000000000000,84.2000000000000,85.6000000000000,86.7000000000000,89.2000000000000,91.7000000000000,91.8000000000000,92.8000000000000,93.2000000000000,94.2000000000000,38.3333333300000,40,40.4000000000000,41.1333333300000,41.3333333300000,41.8000000000000,42.4000000000000,42.8000000000000,44.0666666700000,44.2666666700000,44.4666666700000,45,46.1333333300000,47.8000000000000,48.2666666700000,49.4666666700000,50.4666666700000,51.1333333300000,52.2666666700000,52.5333333300000,52.8000000000000,53.9333333300000,54.3333333300000,54.4666666700000,56.1333333300000,57.0666666700000,57.8000000000000,59.4666666700000,61.1333333300000,61.2000000000000,61.8666666700000,62.1333333300000,62.8000000000000,23,24,24.2400000000000,24.6800000000000,24.8000000000000,25.0800000000000,25.4400000000000,25.6800000000000,26.4400000000000,26.5600000000000,26.6800000000000,27,27.6800000000000,28.6800000000000,28.9600000000000,29.6800000000000,30.2800000000000,30.6800000000000,31.3600000000000,31.5200000000000,31.6800000000000,32.3600000000000,32.6000000000000,32.6800000000000,33.6800000000000,34.2400000000000,34.6800000000000,35.6800000000000,36.6800000000000,36.7200000000000,37.1200000000000,37.2800000000000,37.6800000000000,14.3750000000000,15,15.1500000000000,15.4250000000000,15.5000000000000,15.6750000000000,15.9000000000000,16.0500000000000,16.5250000000000,16.6000000000000,16.6750000000000,16.8750000000000,17.3000000000000,17.9250000000000,18.1000000000000,18.5500000000000,18.9250000000000,19.1750000000000,19.6000000000000,19.7000000000000,19.8000000000000,20.2250000000000,20.3750000000000,20.4250000000000,21.0500000000000,21.4000000000000,21.6750000000000,22.3000000000000,22.9250000000000,22.9500000000000,23.2000000000000,23.3000000000000,23.5500000000000,9.58333333300000,10,10.1000000000000,10.2833333300000,10.3333333300000,10.4500000000000,10.6000000000000,10.7000000000000,11.0166666700000,11.0666666700000,11.1166666700000,11.2500000000000,11.5333333300000,11.9500000000000,12.0666666700000,12.3666666700000,12.6166666700000,12.7833333300000,13.0666666700000,13.1333333300000,13.2000000000000,13.4833333300000,13.5833333300000,13.6166666700000,14.0333333300000,14.2666666700000,14.4500000000000,14.8666666700000,15.2833333300000,15.3000000000000,15.4666666700000,15.5333333300000,15.7000000000000,7.18750000000000,7.50000000000000,7.57500000000000,7.71250000000000,7.75000000000000,7.83750000000000,7.95000000000000,8.02500000000000,8.26250000000000,8.30000000000000,8.33750000000000,8.43750000000000,8.65000000000000,8.96250000000000,9.05000000000000,9.27500000000000,9.46250000000000,9.58750000000000,9.80000000000000,9.85000000000000,9.90000000000000,10.1125000000000,10.1875000000000,10.2125000000000,10.5250000000000,10.7000000000000,10.8375000000000,11.1500000000000,11.4625000000000,11.4750000000000,11.6000000000000,11.6500000000000,11.7750000000000,5.75000000000000,6,6.06000000000000,6.17000000000000,6.20000000000000,6.27000000000000,6.36000000000000,6.42000000000000,6.61000000000000,6.64000000000000,6.67000000000000,6.75000000000000,6.92000000000000,7.17000000000000,7.24000000000000,7.42000000000000,7.57000000000000,7.67000000000000,7.84000000000000,7.88000000000000,7.92000000000000,8.09000000000000,8.15000000000000,8.17000000000000,8.42000000000000,8.56000000000000,8.67000000000000,8.92000000000000,9.17000000000000,9.18000000000000,9.28000000000000,9.32000000000000,9.42000000000000,4.79166666700000,5,5.05000000000000,5.14166666700000,5.16666666700000,5.22500000000000,5.30000000000000,5.35000000000000,5.50833333300000,5.53333333300000,5.55833333300000,5.62500000000000,5.76666666700000,5.97500000000000,6.03333333300000,6.18333333300000,6.30833333300000,6.39166666700000,6.53333333300000,6.56666666700000,6.60000000000000,6.74166666700000,6.79166666700000,6.80833333300000,7.01666666700000,7.13333333300000,7.22500000000000,7.43333333300000,7.64166666700000,7.65000000000000,7.73333333300000,7.76666666700000,7.85000000000000]

xe=[0,1.60000000000000,3.54000000000000,5.43000000000000,6.82000000000000,10.0600000000000,14.2200000000000,17,56.0900000000000,62.2600000000000,68.4300000000000,73.0900000000000,83,90,91.0500000000000,93.7500000000000,96.0900000000000,97.6500000000000,99.5500000000000,100,100,100,100,100,100,100,100,100,100,100,100,100,100,0,0.500000000000000,0.710000000000000,2,2.96000000000000,5.20000000000000,8.08000000000000,10,40.4000000000000,45.2000000000000,50,59.2300000000000,78.8400000000000,87.5000000000000,88.8700000000000,92.4100000000000,94.5600000000000,96,98.6000000000000,98.7000000000000,98.9000000000000,99.5000000000000,99.7000000000000,99.7500000000000,100,100,100,100,100,100,100,100,100,0,0,0.0800000000000000,0.110000000000000,0.150000000000000,0.320000000000000,0.730000000000000,1,6.57000000000000,7.45000000000000,8.33000000000000,21.6600000000000,50,87,88.6800000000000,93,95.9000000000000,97.8400000000000,99.5000000000000,100,100,100,100,100,100,100,100,100,100,100,100,100,100,0,0,0,0,0,0,0.670000000000000,1.12000000000000,13.1900000000000,15.0900000000000,17,27.2400000000000,49,75.7000000000000,80.3800000000000,92.4000000000000,95.8500000000000,98.1500000000000,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,0,0,0,0,0,0,0,2.18000000000000,9.07000000000000,10.1600000000000,11.2500000000000,17.5500000000000,30.9500000000000,67.4000000000000,72.2700000000000,84.7800000000000,90.1600000000000,93.7500000000000,98.8100000000000,100,100,100,100,100,100,100,100,100,100,100,100,100,100,0,0,0,0,0,0,0,0,4.30000000000000,6.10000000000000,12.2000000000000,17.6700000000000,29.3000000000000,59.4000000000000,65.6600000000000,81.7400000000000,88.0800000000000,92.3000000000000,96.3200000000000,97.2600000000000,98.2100000000000,100,100,100,100,100,100,100,100,100,100,100,100,0,0,0,0,0,0,0,0,0,0.820000000000000,1.64000000000000,3.12000000000000,6.25000000000000,23.1000000000000,30.6300000000000,50,66.5600000000000,77.6000000000000,85.7900000000000,87.7100000000000,89.6400000000000,93.8500000000000,95.3400000000000,95.8300000000000,98.6400000000000,100,100,100,100,100,100,100,100,0,0,0,0,0,0,0,0,0,0.600000000000000,6.30000000000000,12.5700000000000,19.3000000000000,31.5200000000000,36.7000000000000,50,58.4000000000000,64,72.3600000000000,74.3300000000000,76.3000000000000,83.5800000000000,86.1400000000000,87,95,96.8600000000000,98.3300000000000,100,100,100,100,100,100,0,0,0,0,0,0,0,0,0,0,0,0,1.80000000000000,6.74000000000000,9.53000000000000,16.7000000000000,25.4300000000000,31.2500000000000,45.3600000000000,48.6800000000000,52,66.0800000000000,71.0400000000000,72.7000000000000,87,91.4000000000000,94.8500000000000,98.9000000000000,99.9600000000000,100,100,100,100,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.67000000000000,5.95000000000000,11.9200000000000,15.9000000000000,26.4400000000000,28.9200000000000,31.4000000000000,51.1300000000000,58.0900000000000,60.4100000000000,82,86.8600000000000,90.6700000000000,95.3700000000000,99.3000000000000,99.3600000000000,100,100,100,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]

CR=[0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120]

y(1)=sqrt((xe-(1-exp(-(x(1)*exp(-(x(2)+x(3)*log(CR))/(8.314*T)))*t^x(4))))/xe)^2

end

The above function is used to find the unknown parameters by optimization procedure like fminsearch.