2) A police detective investigating a murder finds the body of the victim at 9:30 pm. At that time, the temperature of the victims body is 65° F. After 45 minutes, the victims body has cooled to 60° F. The surrounding temperature outside has been constant 50°F for the entire day. Assuming that the victim's body follows Newton's law of cooling : i) Write down a differential equation for the temperature of the victims body (your answer will involve a proportionality constant). ii) Find the general solution (your answer will involve a proportionality constant). iii) Use the provided information to determine the temperature as a function of time, for the victim's body. You may take t = 0 to be 9:30 pm. iv) Typical human body temperature is 98.6° F. Use this to estimate the time of death of the victim.
2) A police detective investigating a murder finds the body of the victim at 9:30 pm. At that time, the temperature of the victims body is 65° F. After 45 minutes, the victims body has cooled to 60° F. The surrounding temperature outside has been constant 50°F for the entire day. Assuming that the victim's body follows Newton's law of cooling : i) Write down a differential equation for the temperature of the victims body (your answer will involve a proportionality constant). ii) Find the general solution (your answer will involve a proportionality constant). iii) Use the provided information to determine the temperature as a function of time, for the victim's body. You may take t = 0 to be 9:30 pm. iv) Typical human body temperature is 98.6° F. Use this to estimate the time of death of the victim.
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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Transcribed Image Text:2) A police detective investigating a murder finds the body of the victim at 9:30 pm. At that time, the temperature of the
victims body is 65° F. After 45 minutes, the victims body has cooled to 60° F. The surrounding temperature outside has
been constant 50°F for the entire day.
Assuming that the victim's body follows Newton's law of cooling :
i)
Write down a differential equation for the temperature of the victims body (your answer will involve a proportionality
constant).
ii)
Find the general solution (your answer will involve a proportionality constant).
iii) Use the provided information to determine the temperature as a function of time, for the victim's body. You may
take t = 0 to be 9:30 pm.
iv) Typical human body temperature is 98.6° F. Use this to estimate the time of death of the victim.
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