# Which is what the temperature difference will do so

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which is what the temperature difference will do. So, we want to analyze the data where t = time elapsed and y = C 69, the temperature difference between the coffee temperature and the room temperature. TABLE 2 t = Time Elapsed (minutes) y = C 69 Temperature Difference (degrees F.) 0 97.0 10 71.5 20 56.2 30 41.3 40 35.5 50 29.4 60 24.9
0 10 20 30 40 50 60 70 0 20 40 60 80 100 120 f(x) = 89.98 exp( − 0.02 x ) R² = 0.98 Temperature Difference between Coffee and Room Time Elapsed (minutes) Temperature Difference (degrees) Exponential Function of Best Fit (using the data in Table 2): y = 89.976 e 0.023 t where t = Time Elapsed (minutes) and y = Temperature Difference (in degrees) (a) Use the exponential function to estimate the temperature difference y when 25 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree. (explanation/work optional) (b) Since y = C 69, we have coffee temperature C = y + 69. Take your difference estimate from part (a) add 69 degrees. Interpret the result by filling in the blank: When 25 minutes have elapsed, the estimated coffee temperature is ________ degrees. (c) Suppose the coffee temperature C is 100 degrees. Then y = C 69 = ____ degrees is the temperature difference between the coffee and room temperatures. (d) Consider the equation _____ = 89.976 e 0.023 t where the ____ is filled in with your answer from part (c). and EXTRA CREDIT (6 pts): Show algebraic work to solve this part (d) equation for t , to the nearest tenth. Interpret your results clearly in the context of the coffee application. [Use additional paper if needed]
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