According to Newton’s Law of Cooling, the rate of change of the temperature of an objectcan be modeled using the following differential equation: dT/dt=−κ(T−A) where T is the temperature of the object (in◦F), A is the room temperature (in◦F), and κ is 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 coroner arrived 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.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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 objectcan be modeled using the following differential equation:

dT/dt=−κ(T−A)

where T is the temperature of the object (in◦F), A is the room temperature (in◦F), and κ is 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 coroner arrived 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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