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)

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)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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