After sitting in a refrigerator for a while, a turkey at a temperature of 34°F is placed on the counter and slowly warms closer to room temperature (70°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
room, as given by the formula below:
T=T, + (T. – T.)e-kt
Ta the temperature surrounding the object
To = the initial temperature of the object
t = the time in minutes
T = the temperature of the object after t minutes
k= decay constant
The turkey reaches the temperature of 46°F after 15 minutes. 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 105 minutes.