Question

The temperature at time t, y(t) in units of 100◦F of a room in the winter...

The temperature at time t, y(t) in units of 100◦F of a room in the winter satisfies the differential equation

dy/dt ={ −y + 1, if heating unit is on

   −y, if heating unit is off }

Suppose the initial temperature is y(0) = 0 at 9a.m.

(Let the time t = 0 corresponds to 9a.m., t = 1 corresponds to 10a.m. and so on.) The heating unit is on from 9 to 10a.m., off from 10 to 11a.m., on again from 11a.m. to noon and so on. What is the room temperature at noon? (Hint: the answer is 71.8◦F.)

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