A detective finds a murder victim at 9 am. The temperature of the body is measured at 90.3◦F. One hour later, the temperature of the body is 89.0◦F. The temperature of the room has been maintained at a constant 68◦F.
(a) Assuming the temperature, T , of the body obeys Newton’s Law of Cooling, write a differential equation for T.
(b) Solve the differential equation to estimate the time the murder occurred.