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Newton’s Law of Cooling states that the temperature of a heated object decreases exponentially over time toward the temperature of the surrounding medium. The temperature u of a heated object at a given time t can be modeled by the following function:
u(t)=T+(u-T)e^kt K<0

where T is the constant temperature of the surrounding medium,
u is the initial temperature of the heated object, and
k is a negative constant for a specific object

Our normal body temperature is usually warmer than the ambient air temperature indoors. Therefore, upon death, the body temperature will exponentially decay according to the function above. For the human body, k = -1/-2.5, if temperature is measured in Fahrenheit.

Q) At 8:30 AM, the police forensic team was called to the Calgary home of a person who had apparently been murdered sometime during the night. In order to estimate the time of death, the person’s body temperature was measured. At 9:00 AM, the body temperature was 84.6 degrees Fahrenheit. Estimate the time of death.

a body after death for a normal body temperature of 98.6 degrees and a constant ambient room temperature of 70 degrees Fahrenheit.

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