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Exercise 2.1.6 A body is found at a certain time and has a temperature of 92.6 degrees Fahren- heit in an environment with ambient temperature 70 degrees. Two hours later the body has a temperature of 90 degrees Fahrenheit. The flu was going around and it was believed the victim was on her way to the drugstore because her roommate said she had a temperature of 102.4 degrees Fahrenheit. If Newton's law of cooling holds, estimate when the person died, relative to the time the body was found. Hint: call the time the body is found t = 0 and solve u' (t) = -k(u(t) -A) with A = 70 and initial condition u(0) = 92.6. Then use u(2) = 90 to find k, and from that figure out at what time u(t) equaled 102.4.

Exercise 2.1.6 A body is found at a certain time and has a temperature of 92.6 degrees Fahren- heit in an environment with ambient temperature 70 degrees. Two hours later the body has a temperature of 90 degrees Fahrenheit. The flu was going around and it was believed the victim was on her way to the drugstore because her roommate said she had a temperature of 102.4 degrees Fahrenheit. If Newton's law of cooling holds, estimate when the person died, relative to the time the body was found. Hint: call the time the body is found t = 0 and solve u' (t) = -k(u(t) -A) with A = 70 and initial condition u(0) = 92.6. Then use u(2) = 90 to find k, and from that figure out at what time u(t) equaled 102.4.

Advanced Engineering Mathematics
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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Exercise 2.1.6 A body is found at a certain time and has a temperature of 92.6 degrees Fahren- heit in an environment with ambient temperature 70 degrees. Two hours later the body has a temperature of 90 degrees Fahrenheit. The flu was going around and it was believed the victim was on her way to the drugstore because her roommate said she had a temperature of 102.4 degrees Fahrenheit. If Newton's law of cooling holds, estimate when the person died, relative to the time the body was found. Hint: call the time the body is found t = 0 and solve u' (t) = -k(u(t) -A) with A = 70 and initial condition u(0) = 92.6. Then use u(2) = 90 to find k, and from that figure out at what time u(t) equaled 102.4.
Transcribed Image Text:Exercise 2.1.6 A body is found at a certain time and has a temperature of 92.6 degrees Fahren- heit in an environment with ambient temperature 70 degrees. Two hours later the body has a temperature of 90 degrees Fahrenheit. The flu was going around and it was believed the victim was on her way to the drugstore because her roommate said she had a temperature of 102.4 degrees Fahrenheit. If Newton's law of cooling holds, estimate when the person died, relative to the time the body was found. Hint: call the time the body is found t = 0 and solve u' (t) = -k(u(t) -A) with A = 70 and initial condition u(0) = 92.6. Then use u(2) = 90 to find k, and from that figure out at what time u(t) equaled 102.4.
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