After sitting in a refrigerator for a while, a turkey at a temperature of 39°F is placed on the counter and slowly warms closer to room temperature (73°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 = Ta + (To - Ta)e-hit
To = the temperature surrounding the object
To = the initial temperature of the object
† = the time in minutes
T = the temperature of the object after t minutes
k = decay constant
The turkey reaches the temperature of 51°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 90 minutes.
Enter only the final temperature into the input box.