A dead body was discovered shortly before midnight. At exactly midnight, the temperature of the body was 85°F. Four hours later, the body had caaled to 74°F. If the room where the body was found was a constant 68°F, what was the time of death? Solve this problem by first setting up the differential equation that describes this situation, then find its solution to answer the question. Note: Newton's Law of cooling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and its surroundings. (Take normal body temperature to be 98.6°F)

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Chapter2: Second-order Linear Odes
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A dead body was discovered shortly before midnight. At exactly midnight, the temperature of the body was 85°F.
Four hours later, the body had cooled to 74°F. If the room where the body was found was a constant 68°F, what
was the time of death? Solve this problem by first setting up the differential equation that describes this situation,
then find its solution to answer the question. Note: Newton's Law of coaling states that the rate of change of
temperature of an object is proportional to the difference in temperature between the object and its surroundings.
(Take normal body temperature to be 98.6°F)
Transcribed Image Text:A dead body was discovered shortly before midnight. At exactly midnight, the temperature of the body was 85°F. Four hours later, the body had cooled to 74°F. If the room where the body was found was a constant 68°F, what was the time of death? Solve this problem by first setting up the differential equation that describes this situation, then find its solution to answer the question. Note: Newton's Law of coaling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and its surroundings. (Take normal body temperature to be 98.6°F)
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