A cup of hot coffee was placed in a room maintained at a constant temperature of 69 degrees. The coffee temperature was recorded periodically, in table 1.

TABLE 1 REMARKS: TABLE 2 Common sense tells us that the coffee will be cooling off y = C-69 t = Time C = Coffee and its temperature will decrease and approach the ambient t = Time Temperature Elapsed Temperature temperature of the room, 69 degrees. Elapsed Difference (minutes) (degrees F.) (degrees F.) (minutes) So, the temperature difference between the coffee 166.0 temperature and the room temperature will decrease to 0. 0 97.0 0 10 140.5 10 71.5 20 125.2 We will fit the temperature difference data (Table 2) to an 20 56.2 30 110.3 exponential curve of the form y = A e-bi. 30 41.3 40 40 35.5 104.5 50 Notice that as t gets large, y will get closer and closer to 0, 98.4 which is what the temperature difference will do. 50 29.4 60 93.9 So, we want to analyze the data where t = time elapsed 60 24.9 and y = C - 69, the temperature difference between the coffee temperature and the room temperature. 120 Temperature Difference (degrees) 100 Temperature Difference between Coffee and Room 80 y = 89.976e-0.023t 60 R2 = 0.9848 40 20 O 0 10 20 30 40 50 60 70 Time Elapsed (minutes) Exponential Function of Best Fit (using the data in Table 2): y= 89.976 e - 0.025 where t = Time Elapsed (minutes) and y = Temperature Difference (in degrees)