According to Newton’s Law of Cooling, the rate of change of the temperature of an objectcan be modeled using the following differential equation: dTdt=−κ(T−A) where Tis the temperature of the object (in◦F),Ais the room temperature (in◦F), andκis the constant of proportionality. (a) Use an appropriate method to solve the differential equation. Remember that κ and A are constants. (b) Use your answer to (a) to solve the following: On a crime show, a dead body is discovered in a hotel room. A forensic technician recordedthat the victim’s body temperature was 91.4◦F at 6:00 pm. One hour later, the coronerarrived and found that the victim’s body temperature had fallen to 88.7◦F. If the thermostatin the hotel room is set at 68◦F, determine when the victim was murdered.(Assume the victim was a healthy 98.6◦F at the time of death.)
According to Newton’s Law of Cooling, the rate of change of the temperature of an objectcan be modeled using the following
dTdt=−κ(T−A)
where Tis the temperature of the object (in◦F),Ais the room temperature (in◦F), andκis the constant of proportionality.
(a) Use an appropriate method to solve the differential equation. Remember that κ and A are constants.
(b) Use your answer to (a) to solve the following:
On a crime show, a dead body is discovered in a hotel room. A forensic technician recordedthat the victim’s body temperature was 91.4◦F at 6:00 pm. One hour later, the coronerarrived and found that the victim’s body temperature had fallen to 88.7◦F. If the thermostatin the hotel room is set at 68◦F, determine when the victim was murdered.(Assume the victim was a healthy 98.6◦F at the time of death.)
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