QUESTION 2. Submit all steps, code, script, solutions, plots, etc. [Mark: 3.5] Newton's Law of Cooling Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of its surrounding medium, dT dt =-k(T-T) where T = temperature of the body in C, t = time in hours, K = proportionality constant in s,T surrounding temperature in C. = To create a chalice, a piece of alloy is heated up to 1000C and then cooled in a pool of water to 7, C before forging. The artist blacksmith repeats this process until a beautiful goblet is produced. Estimate the time it takes for the 1000C alloy to be immersed in the pool of water at 25C using Euler method. Invoke Newton's law of cooling, assuming k = 0.0, s and At = 10 S, 1S. Here, , , are the smallest, second smallest, and third smallest non-zero digits, respectively, of your student ID. E.g., ID = 110 985 247 gives a = 1, = 2, and = 4, i.e., the alloy is to be cooled to a 712C, k = 0.04 s. Euler's Method New value = Old value + Slope > Step size