Chapter 5.5, Problem 57E

Forensics 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

$t=-10\ln \frac{T-70}{98.6-70}$

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.