Question 122245
A cup of coffee is poured and left to cool on the counter. The formula that represents the temperature of the coffee over time is given by T=80(0.9)^(x/2)+20 where T is temperature in degrees celcius, and x is time in minutes. 
a) What was the initial temperature of the coffee?
T(x) = 80(0.9)^(x/2)+20
T(0) = 80(0.9)^(0/2)+20 = 80*1+20= 100 degrees Celcius.
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b) How quickly is it cooling?
T(1) = 80(0.9)^(1/2) 75.89 degrees
So, in one minute the temperature decreased 24.11 degrees.
Comment: The decrease is not linear as the function is exponential. 
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c) What is the coolest temperature the coffee will reach? Why?
As x getslarger 0.9^(x/2) gets smaller and smaller.
To T gets closer and closer to 20 degrees.
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d) What is the temperature of the coffee after 10 minutes?
T(10) = 80(0.9)^5 + 20 = 67.2392 degrees Celsius.
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Comment: These termperatures do not look realistic. Coffee at
100 degrees Celsius would be at the boiling point.
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Cheers,
Stan H.