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?
b) How quickly is it cooling?
c) What is the coolest temperature the coffee will reach? How quickly?
d) What is the temperature of the coffee after 10 minutes?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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