SOLUTION: A cup of coffee has cooled from 92degreesC to 50degreesC after 13 minutes in a room at 24degreesC. How long will it take to cool to 30degrees​C?
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-> SOLUTION: A cup of coffee has cooled from 92degreesC to 50degreesC after 13 minutes in a room at 24degreesC. How long will it take to cool to 30degrees​C?
Thank you!
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Question 1126746: A cup of coffee has cooled from 92degreesC to 50degreesC after 13 minutes in a room at 24degreesC. How long will it take to cool to 30degreesC?
Thank you! Answer by ikleyn(52803) (Show Source):
The Newton law of cooling states that the temperature of the cup of coffee in the room is this function of time t
T(t) = = .
where "k" is the decay constant.
At t= 13 minutes T(t)= 50, which gives you an equation to find the decay constant k:
50 = 24 + 68*e^(-k*13)
68*e^(-k*13) = 50 - 24 = 26
e^(-13k) = = 0.3823
- 13k = ln(0.3823)
k = = 0.074.
Thus the decay constant k is found.
The last step is to find the time under the question. For it, you have this equation
T(t) = = 30
e(-0.074*t) = = 0.088
-0.074*t = ln(0.088)
t = = 32.8
Answer. 32.8 minutes counting from the very beginning time moment.
