(a) The cooling problem in Section 4.1 has an exact mathematical solution. The temperature T (t) at time t is given by the formula where T 0 is the initial temperature. Insert this formula into the...

(a) The cooling problem in Section 4.1 has an exact mathematical solution. The temperature T (t) at time t is given by the formula

where T₀
is the initial temperature. Insert this formula into the cool method of Fridge and display it alongside the numerical solution. Your enlarged table of output should look something like this:

(b) The numerical solution generated by Equation (4.3) gets more accurate as dt gets smaller. That is because Equation (4.5) (the exact solution) is derived from Equation (4.3) in the limit as dt → 0.

Table 4.1 compares results for dt = 1 and dt = 0.1, with opInt = 5. On the other hand, as dt gets larger, the numerical solution becomes less and less accurate and eventually becomes meaningless. Experiment with a few larger values of dt.