SOLUTION: A cup of coffee at 85°C is placed in a freezer at 0°C.The temperature of the coffee decreases exponentially, so that after 5 minutes it is 30°C.
(a)What is its temperature afte
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Question 1163599: A cup of coffee at 85°C is placed in a freezer at 0°C.The temperature of the coffee decreases exponentially, so that after 5 minutes it is 30°C.
(a)What is its temperature after 3 minutes?
(b)Find by trial how long it will take for the temperature to drop ton5°C.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ T_oe^{-\lambda t})
Where 
is the temperature in degrees C as a function of time, 
, in minutes, 
is the initial temperature at time 
, and 
is the decay constant.
The initial condition is
\ =\ 85e^{-0\lambda}\ =\ 85^\circ)
The 5 minute condition is:
\ =\ 85e^{-5\lambda}\ =\ 30^\circ)
\ =\ \ln\(\frac{30}{85}\))
\,-\,\ln(17))
\,-\,\ln(17)}{5})
Once you have done the indicated arithmetic to calculate a sufficiently precise approximation of to suit your particular application, you can use that value in the basic function to calculate temperature at a given time or solve for time given a temperature.
John
My calculator said it, I believe it, that settles it
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