This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 50°F. (a) Find a function T(t) that models the temperature t hours after death. T(t) = 60 + 38.6e-0.19471 (b) If the temperature of the body is now 71°F, how long ago was the time of death? (Round your answer to the nearest whole number.) 6 X hr

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 31PT: A bottle of soda with a temperature of 71 Fahrenheit was taken off a shelf and placed ina...
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This exercise uses Newton's Law of Cooling.
Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been
determined experimentally that the constant in Newton's Law of Cooling is approximatelyk = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 50°F.
(a) Find a function T(t) that models the temperature t hours after death.
T(t) = 60 + 38.6e
,-0.1947t
(b) If the temperature of the body is now 71°F, how long ago was the time of death? (Round your answer to the nearest whole number.)
6.
hr
Transcribed Image Text:This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximatelyk = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 50°F. (a) Find a function T(t) that models the temperature t hours after death. T(t) = 60 + 38.6e ,-0.1947t (b) If the temperature of the body is now 71°F, how long ago was the time of death? (Round your answer to the nearest whole number.) 6. hr
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