At 8: 30 a. m., a coroner went 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 85.7°f and at 11: 00 a. m. the temperature was 82.8°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 comes 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.