Question

Suppose that your air conditioner fails on Sunday at midnight (t0 = 0),
and you cannot afford to have it repaired until payday at the end of
the month. Assume that the outside temperature varies according to
the function

A(t) = 80 5 cos(π/12)-5√3sin(π/12t)

and that your inside temperature, u(t) obeys Newton’s law of cooling
and is governed by the differential equation
du/dt= -0.2(u-A(t))

(a) If your indoor temperature when the air conditioner failed was
70◦F , determine the dynamics of temperature inside your apart-
ment over time. i.e. find a particular solution to the initial value
problem.
(b) What will the temperature inside the apartment be, 24 hours after
the break down?
(c) In the long run (t → ∞), what is the maximum and minimum
temperature you can anticipate inside your apartment?

Answer 1