SOLUTION: Hello, I don't know how to solve this problem: A cup of coffee which is initially at a temperature of 154 degrees Fahrenheit is placed in a room which is at a constant tempe

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Question 929060: Hello,
I don't know how to solve this problem:
A cup of coffee which is initially at a temperature of 154 degrees Fahrenheit is placed in a room which is at a constant temperature of 71 degrees. In 10 minutes, the coffee has cooled to 133 degrees. Find the Newton's Law of Cooling formula that models the coffee's temperature in t minutes. Determine to the nearest minute how long it will take the coffee to cool to a temperature of 100 degrees Fahrenheit.
Thank you in advance,
Ryan M.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First off, find Newton's law of cooling,

Use the two data points given to find k.
At t=0,T=154
At t=10,T=133,
k%280-10%29=-ln%28%28154-71%29%2F%28133-71%29%29
-10k=-0.291716
k=0.02917
.
.
.
So now find t when T=100,
Then,
0.02917%280-t%29=-ln%28%28154-71%29%2F%28100-71%29%29
-0.02917t=-1.0515
t=36.05minutes
To the nearest minute,
t=36