10. EXPONENTIAL REGRESSION

Data: A cup of hot coffee was placed in a room maintained at a constant temperature of 75 degrees, and the coffee temperature was recorded periodically, in Table 1.

REMARKS:

Common sense tells us that the coffee will be cooling off and its temperature will decrease and approach the ambient temperature of the room, 75 degrees.

So, the temperature difference between the coffee temperature and the room temperature will decrease to 0.

We will fit the temperature difference data (Table 2) to an exponential curve of the form y=Ae^-bt.

Notice that astgets large,ywill get closer and closer to 0, which is what the temperature difference will do.

So, we want to analyze the data wheret= time elapsed andy=C - 75, the temperature difference between the coffee temperature and the room temperature.

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