document.write( "Question 1039932: I could really use some help on this please!\r
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\n" ); document.write( "\n" ); document.write( "EXPONENTIAL REGRESSION
\n" ); document.write( "Data: A cup of hot coffee was placed in a room maintained at a constant temperature of 72 degrees, and the coffee temperature was recorded periodically, in Table 1. \r
\n" ); document.write( "\n" ); document.write( "t = Time Elapsed
\n" ); document.write( "(minutes) C = Coffee
\n" ); document.write( "Temperature (degrees F.)
\n" ); document.write( "0----- 169.0
\n" ); document.write( "10----- 143.5
\n" ); document.write( "20----- 128.2
\n" ); document.write( "30----- 113.3
\n" ); document.write( "40----- 107.5
\n" ); document.write( "50----- 101.4
\n" ); document.write( "60----- 96.9
\n" ); document.write( "TABLE 1 REMARKS:
\n" ); document.write( "Common sense tells us that the coffee will be cooling off and its temperature will decrease and approach the ambient temperature of the room, 72 degrees.\r
\n" ); document.write( "\n" ); document.write( "So, the temperature difference between the coffee temperature and the room temperature will decrease to 0.
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\n" ); document.write( "We will fit the temperature difference data (Table 2) to an exponential curve of the form y = A e^-bt. \r
\n" ); document.write( "\n" ); document.write( "Notice that as t gets large, y will get closer and closer to 0, which is what the temperature difference will do.
\n" ); document.write( "So, we want to analyze the data where t = time elapsed and y = C - 72, the temperature difference between the coffee temperature and the room temperature. TABLE 2
\n" ); document.write( "t = Time Elapsed (minutes) y = C - 72 Temperature
\n" ); document.write( "Difference
\n" ); document.write( "(degrees F.)
\n" ); document.write( "0----- 97.0
\n" ); document.write( "10----- 71.5
\n" ); document.write( "20----- 56.2
\n" ); document.write( "30----- 41.3
\n" ); document.write( "40----- 35.5
\n" ); document.write( "50----- 29.4
\n" ); document.write( "60----- 24.9\r
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\n" ); document.write( "\n" ); document.write( "Exponential Function of Best Fit (using the data in Table 2):
\n" ); document.write( " y = 89.976 e^-0.023 t where t = Time Elapsed (minutes) and y = Temperature Difference (in degrees)\r
\n" ); document.write( "\n" ); document.write( "(a) Use the exponential function to estimate the temperature difference y when 15 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree. (explanation/work optional)\r
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\n" ); document.write( "\n" ); document.write( "(b) Since y = C - 72, we have coffee temperature C = y + 72. Take your difference estimate from part (a) and add 72 degrees. Interpret the result by filling in the blank:
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\n" ); document.write( " When 15 minutes have elapsed, the estimated coffee temperature is ________ degrees.\r
\n" ); document.write( "\n" ); document.write( "(c) Suppose the coffee temperature C is 105 degrees. Then y = C - 72 = ____ degrees is the temperature difference between the coffee and room temperatures.
\n" ); document.write( "(d) Consider the equation _____ = 89.976 e^-0.023t where the ____ is filled in with your answer from part (c).\r
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\n" ); document.write( "\n" ); document.write( "Any help you can offer on this would be very helpful! Thank you so much!
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Algebra.Com's Answer #654698 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "a. Substitute 15 for t in the exponential equation and then do the indicated arithmetic. Given the precision shown in the table, you can probably round to the nearest 10th of a degree.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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