After sitting in a refrigerator for a while, a turkey at a temperature of 40, degrees40∘40∘F is placed on the counter and slowly warms closer to room temperature (69, degrees69∘69∘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:

After sitting in a refrigerator for a while, a turkey at a temperature of 40, degrees40∘40∘F is placed on the counter and slowly warms closer to room temperature (69, degrees69∘69∘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, equals, T, start subscript, a, end subscript, plus, left bracket, T 0, minus, T, start subscript, a, end subscript, right bracket, e, start superscript, minus, k, t, end superscript

�=��+(�0−��)�−��T=Ta+(T0−Ta)e−kt

T, start subscript, a, end subscript, equals��=Ta= the temperature surrounding the object
T 0, equals�0=T0= the initial temperature of the object
t, equals�=t= the time in minutes
T, equals�=T= the temperature of the object after t�t minutes
k, equals�=k= decay constant

The turkey reaches the temperature of 48, degrees48∘48∘F after 25 minutes. Using this information, find the value of k�k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 105 minutes.

Enter only the final temperature into the input box.

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Step 2: Determine the value of k:

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Step 3: Determine the Fahrenheit temperature of the turkey after 105 minutes:

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