A detective is called to the scene of a crime where a dead body has just been found. She arrives on the scene at 10:23 pm and begins her investigation. Immediately, the temperature of the body is taken and is found to be 80°F. The detective checks the programmable thermostat and finds that the room has been kept at a constant 68°F for the past 3 days. After evidence from the crime scene is collected, the temperature of the body is taken once more and found to be 78.5°F. This last temperature reading was taken exactly one hour after the first one. (a) Solve Newton's Law of Cooling as modeled by the first-order differential equation dT = -k(T-Tm) to express the temperature T of an object at time t. dt (b) Apply the given information to part (a) to arrive at a specific model to be used in the context of this crime scene investigation. (c) Find when the victim died, assuming that the victim's body was a normal 98.6°F prior to death.
A detective is called to the scene of a crime where a dead body has just been found. She arrives on the scene at 10:23 pm and begins her investigation. Immediately, the temperature of the body is taken and is found to be 80°F. The detective checks the programmable thermostat and finds that the room has been kept at a constant 68°F for the past 3 days. After evidence from the crime scene is collected, the temperature of the body is taken once more and found to be 78.5°F. This last temperature reading was taken exactly one hour after the first one. (a) Solve Newton's Law of Cooling as modeled by the first-order differential equation dT = -k(T-Tm) to express the temperature T of an object at time t. dt (b) Apply the given information to part (a) to arrive at a specific model to be used in the context of this crime scene investigation. (c) Find when the victim died, assuming that the victim's body was a normal 98.6°F prior to death.
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Transcribed Image Text:A detective is called to the scene of a crime where a dead body has just been found. She
arrives on the scene at 10:23 pm and begins her investigation. Immediately, the
temperature of the body is taken and is found to be 80°F. The detective checks the
programmable thermostat and finds that the room has been kept at a constant 68°F for the
past 3 days. After evidence from the crime scene is collected, the temperature of the body is
taken once more and found to be 78.5°F. This last temperature reading was taken exactly
one hour after the first one.
(a) Solve Newton's Law of Cooling as modeled by the first-order differential equation
−k(T – Tm) to express the temperature T of an object at time t.
dT
dt
=
(b) Apply the given information to part (a) to arrive at a specific model to be used in the
context of this crime scene investigation.
(c) Find when the victim died, assuming that the victim's body was a normal 98.6°F prior to
death.
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