According to Newton's Law of Cooling, the rate of change of the temperature of an object can be modeled using the following differential equation: dT — к(Т — А); dt where T is the temperature of the object (in °F), A is the room temperature (in °F), and k is the constant of proportionality. (a) Use an appropriate method to solve the differential equation. Remember that k 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 recorded that the victim's body temperature was 91.4°F at 6:00 pm. One hour later, the coroner arrived and found that the victim's body temperature had fallen to 88.7°F. If the thermostat in 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.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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According to Newton's Law of Cooling, the rate of change of the temperature of an object
can be modeled using the following differential equation:
dT
— к(Т — А);
dt
where T is the temperature of the object (in °F), A is the room temperature (in °F), and k is the
constant of proportionality.
(a) Use an appropriate method to solve the differential equation.
Remember that к апd 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 recorded
that the victim's body temperature was 91.4°F at 6:00 pm. One hour later, the coroner
arrived and found that the victim's body temperature had fallen to 88.7° F. If the thermostat
in 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.)
Transcribed Image Text:According to Newton's Law of Cooling, the rate of change of the temperature of an object can be modeled using the following differential equation: dT — к(Т — А); dt where T is the temperature of the object (in °F), A is the room temperature (in °F), and k is the constant of proportionality. (a) Use an appropriate method to solve the differential equation. Remember that к апd 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 recorded that the victim's body temperature was 91.4°F at 6:00 pm. One hour later, the coroner arrived and found that the victim's body temperature had fallen to 88.7° F. If the thermostat in 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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