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A forensic method for estimating the time of death of a body is based on the law of newton of cooling, given by the governing equation dT = -k(T – A(t)), dt Where k > 0 is the rate at which heat is lost from the body and A(t) is the temperature environment. The idea is to measure the body temperature at two different times, in order to to calculate the constant K, and thus "reverse extrapolate" to the temperature of the living body T = 37°C. Suppose a body was found in a room in which the ambient temperature is kept constant at 24°C. At eight in the morning the measured body temperature is 28°C, after one hour the temperature is found to have dropped to 26°C. show that integrating the measured body temperature at two different times t, and t2, will result in T(t,) = A + [T(t,) – A]e¬k(t2=t;). Calculate k and determine the time of death. Note:Newton's law of cooling

A forensic method for estimating the time of death of a body is based on the law of newton of cooling, given by the governing equation dT = -k(T – A(t)), dt Where k > 0 is the rate at which heat is lost from the body and A(t) is the temperature environment. The idea is to measure the body temperature at two different times, in order to to calculate the constant K, and thus "reverse extrapolate" to the temperature of the living body T = 37°C. Suppose a body was found in a room in which the ambient temperature is kept constant at 24°C. At eight in the morning the measured body temperature is 28°C, after one hour the temperature is found to have dropped to 26°C. show that integrating the measured body temperature at two different times t, and t2, will result in T(t,) = A + [T(t,) – A]e¬k(t2=t;). Calculate k and determine the time of death. Note:Newton's law of cooling

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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A forensic method for estimating the time of death of a body is based on the law of newton of cooling, given by the governing equation dT = -k(T – A(t)), dt Where k > 0 is the rate at which heat is lost from the body and A(t) is the temperature environment. The idea is to measure the body temperature at two different times, in order to to calculate the constant K, and thus "reverse extrapolate" to the temperature of the living body T = 37°C. Suppose a body was found in a room in which the ambient temperature is kept constant at 24°C. At eight in the morning the measured body temperature is 28°C, after one hour the temperature is found to have dropped to 26°C. show that integrating the measured body temperature at two different times t, and t2, will result in T(t,) = A + [T(t,) – A]e¬k(t2=t;). Calculate k and determine the time of death. Note:Newton's law of cooling
Transcribed Image Text:A forensic method for estimating the time of death of a body is based on the law of newton of cooling, given by the governing equation dT = -k(T – A(t)), dt Where k > 0 is the rate at which heat is lost from the body and A(t) is the temperature environment. The idea is to measure the body temperature at two different times, in order to to calculate the constant K, and thus "reverse extrapolate" to the temperature of the living body T = 37°C. Suppose a body was found in a room in which the ambient temperature is kept constant at 24°C. At eight in the morning the measured body temperature is 28°C, after one hour the temperature is found to have dropped to 26°C. show that integrating the measured body temperature at two different times t, and t2, will result in T(t,) = A + [T(t,) – A]e¬k(t2=t;). Calculate k and determine the time of death. Note:Newton's law of cooling
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