Question

dT/dt = k(T − A), where T is the temperature of the object, t is time,...

dT/dt = k(T − A), where T is the temperature of the object, t is time, k is the proportionality constant, and A is the constant ambient temperature. T (t) = A + Ce^kt is the general solution. Apply the solution to the following scenario: A Police Department officer discovered a corpse in a downtown alley at 1130pm on a night where the constant temperature was 40 degrees Fahrenheit. As she had been trained to do, she immediately recorded the body temperature of the corpse: 93 degrees Fahrenheit. She took the temperature of the corpse again at midnight: 90 degrees Fahrenheit. Assuming that the body’s temperature at the time of death was 98.6 degrees Fahrenheit, at what time did death occur? Give an exact answer and an estimate to the nearest minute.

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