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 350°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 +(T. – T.)e-kt
To = the temperature surrounding the object
To = the initial temperature of the object
t = the time in hours
T = the temperature of the object after t hours
k=decay constant
The turkey reaches the temperature of 126°F after 3 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.