Newton’s Law of Cooling/Warming As shown in Figure 3.3.11, a small metal bar is plac...

Newton’s Law of Cooling/Warming As shown in Figure 3.3.11, a small metal bar is placed inside container A, and container A then is placed within a much larger container B. As the metal bar cools, the ambient temperature T_A(t) of the medium within container A changes according to Newton’s law of cooling. As container A cools, the temperature of the medium inside container B does not change significantly and can be considered to be a constant T_B. Construct a mathematical

model for the temperatures T(t) and T_A(t), where T(t) is the temperature of the metal bar inside container A. As in Problems 1 and 18, this model can be solved by using prior knowledge. Find a solution of the system subject to the initial conditions T(0) = T₀, T_A(0) = T₁.

Reference: Problem 18

The system in Problem 17, like the system in (2), can be solved with no advanced knowledge. Solve for x(t) and y(t) and compare their graphs with your sketches in Problem 17. Determine the limiting values of x(t) and y(t) as Explain why the answer to the last question makes intuitive sense.