After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temperature of 71°F. Newton's Law
of Cooling explains that the temperature of the cup of water will decrease
proportionally to the difference between the temperature of the water and the
temperature of the room, as given by the formula below:
T = Ta + (T. – T.)e-kt
Τα
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 cup of water reaches the temperature of 197°F after 2.5 minutes. Using
this information, find the value of k, to the nearest thousandth. Use the
resulting equation to determine the Fahrenheit temperature of the cup of
water, to the nearest degree, after 5.5 minutes.
Enter only the final temperature into the input box.