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Use the formula to estimate the time of death of the person

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Question

At 8:30 a.m., a coroner was called to the home of a person who had died during the night. In order to estimate the time of death, the coroner took the person's temperature twice. At 9:00 a.m. the temperature was 84.2°F, and at 11:00 a.m. the temperature was 81.6°F. From these two temperatures, the coroner was able to determine that the time elapsed since death and the body temperature were related by the formula

t = −10 ln

T − 70

98.6 − 70

where t is the time in hours elapsed since the person died and T is the temperature (in degrees Fahrenheit) of the person's body. (This formula is derived from a general cooling principle called Newton's Law of Cooling. It uses the assumptions that the person had a normal body temperature of 98.6°F at death, and that the room temperature was a constant 70°F.) Use the formula to estimate the time of death of the person. (Round your answer to the nearest hour.)

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