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Newton\'s law of cooling states that the rate of change in the temperature T of

ID: 2854867 • Letter: N

Question

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:

Explanation / Answer

dT/dt=k(Mt-Tt)

T=Mt+(T(0)-Mt)

T=70+(100-70)e^kt

T(1)=70+30e^1 ,given t=1min,k=1min^-1

T(1)=70+30e=70+30×2.71

T(1)=151.3

T(2)=70+30e^2

T(2)==70+30×2.71^2

T(2)=290