Newtons law of cooling states that the rate of change in the

Newton\'s law of cooling states that the rate of change in the temperature T of a body is proportional to the difference between the temperature of the medium M and the temperature of the body. That is, dT/dt = k(M(t) - T(t)) where k is a constant. Let k = 1/min and the temperature of the medium be constant, M(t) = 70 degree. If the body is initially at 100 degree, use a spreadsheet and Euler\'s method with h = 0.1. to approximate the temperature of the body after: 1 minute. 2 minutes. Enter your answers to the tenth\'s place. By Euler\'s method: T(1) = T(2) =

Solution

T(1) =80.46

T(2) =73.65

T(2) =73.65              n          Yn            tn     f(tn,yn)          h          dely        yn+1 0 100 0.1 -30 0.1 -3 97 1 97 0.2 -27 0.1 -2.7 94.3 2 94.3 0.3 -24.3 0.1 -2.43 91.87 3 91.87 0.4 -21.87 0.1 -2.187 89.683 4 89.683 0.5 -19.683 0.1 -1.9683 87.7147 5 87.7147 0.6 -17.7147 0.1 -1.77147 85.94323 6 85.94323 0.7 -15.9432 0.1 -1.59432 84.34891 7 84.34891 0.8 -14.3489 0.1 -1.43489 82.91402 8 82.91402 0.9 -12.914 0.1 -1.2914 81.62261 9 81.62261 1 -11.6226 0.1 -1.16226 80.46035 10 80.46035 1.1 -10.4604 0.1 -1.04604 79.41432 11 79.41432 1.2 -9.41432 0.1 -0.94143 78.47289 12 78.47289 1.3 -8.47289 0.1 -0.84729 77.6256 13 77.6256 1.4 -7.6256 0.1 -0.76256 76.86304 14 76.86304 1.5 -6.86304 0.1 -0.6863 76.17673 15 76.17673 1.6 -6.17673 0.1 -0.61767 75.55906 16 75.55906 1.7 -5.55906 0.1 -0.55591 75.00315 17 75.00315 1.8 -5.00315 0.1 -0.50032 74.50284 18 74.50284 1.9 -4.50284 0.1 -0.45028 74.05256 19 74.05256 2 -4.05256 0.1 -0.40526 73.6473 20 73.6473 2.1 -3.6473 0.1 -0.36473 73.28257