After sitting out of a refrigerator for a while, a turkey at room temperature ( 70°F) is placed into an oven. The oven temperature is 345°F. Newton's Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the oven, as given by the formula below: T = T, + (To – Ta)e - Ta = the temperature surrounding the object To = the initial temperature of the object the time in hours the temperature of the object after t hours k = decay constant T The turkey reaches the temperature of 120°F after 2.5 hours. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 6 hours.

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Chapter1: Units, Trigonometry. And Vectors
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After sitting out of a refrigerator for a while, a turkey at room temperature (
70°F) is placed into an oven. The oven temperature is 345°F. Newton's Law
of Heating explains that the temperature of the turkey will increase
proportionally to the difference between the temperature of the turkey and
the temperature of the oven, as given by the formula below:
T = Ta + (To – Ta)e¬kt
а
Ta = the temperature surrounding the object
the initial temperature of the object
To
t = the time in hours
T = the temperature of the object after t hours
k = decay constant
The turkey reaches the temperature of 120°F after 2.5 hours. Using this
information, find the value of k, to the nearest thousandth. Use the resulting
equation to determine the Fahrenheit temperature of the turkey, to the
nearest degree, after 6 hours.
Transcribed Image Text:After sitting out of a refrigerator for a while, a turkey at room temperature ( 70°F) is placed into an oven. The oven temperature is 345°F. Newton's Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the oven, as given by the formula below: T = Ta + (To – Ta)e¬kt а Ta = the temperature surrounding the object the initial temperature of the object To t = the time in hours T = the temperature of the object after t hours k = decay constant The turkey reaches the temperature of 120°F after 2.5 hours. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 6 hours.
Expert Solution
Step 1

T = 120°FTa = 345°FT0 = 70°Ft = 2.5 hk = ?

 

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