Explanation Given: The body temperature was 98 ° F when the person died and air temperature was constant at 40 ° F all night and the body temperature was 80 ° F at 7 A .M . and 72 ° F at 8 A .M . . Formula used: The exponential decrease of temperature difference is given by relation, A = A 0 e r t where A 0 is the initial temperature difference, A is the temperature difference after a particular time t and r is the rate of decrease of temperature difference. Calculation: The initial temperature difference of the body with air is given by, A 0 = 80 − 40 = 40 Then, the body temperature was 72 ° F at 8 A .M . when the country coroner examined the body. Thus, at 8 A .M . , the difference in body temperatures is given by, A = 0 72 − 40 = 32 Consider the formula for the exponential decrease of temperature difference, A = A 0 e r t Substitute the values in the formula to get the value of r , 32 = 40 ( e 1 ⋅ r ) r = ln ( 32 40 ) r ≈ − 0

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ISBN: 9780321916600

Author: Mark Dugopolski

Publisher: PEARSON

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Chapter 4.4, Problem 87E

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To calculate: The approximate time of death if the body temperature was 98°F when the person died and the temperature difference between the body and the air decreases exponentially.

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Chapter 4.4, Problem 86E

Chapter 4.4, Problem 88E

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The approximate time of death if the body temperature was 98 ° F when the person died and the temperature difference between the body and the air decreases exponentially.

Solution Summary: The author calculates the approximate time of death if the body temperature was 98°F when the person died and air temperature decreased exponentially.

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To calculate: The approximate time of death if the body temperature was 98°F when the person died and the temperature difference between the body and the air decreases exponentially.

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