Suppose that your air conditioner fails on Sunday at midnight(t0 = 0), and you cannot afford to have it repaired until payday atthe end of the month. Assume that the outside temperature variesaccording to the function.
A(t)= 80 ? 5 cos(?/12t)-5?3sin(?/12t)
and that your inside temperature, u(t) obeys Newton’s law ofcooling and is governed by the differential equation
du/dt=?0.2(u ? A(t))
(a) If your indoor temperature when the air conditioner failedwas 70?F, determine the dynamics of temperature inside your apart-ment over time. i.e. find a particular solution to the initialvalue problem.
(b) What will the temperature inside the apartment be, 24 hoursafter the break down?
(c) In the long run (t ? ?), what is the maximum and minimumtemperature you can anticipate inside your apartment?
(d) Plot the graph of the outdoor and indoor temperature on thesame axis and comment on how long it takes for the indoortemperature to reach a maximum after the outdoor temperaturepeaks.
