Name:_________________________
Coffee Experiment
A cup of hot coffee is left standing on a table in a room where the temperature is
70 degrees Fahrenheit. The temperature of the coffee is measured every minute
and the results are shown in the table below. Find a function of time that best fits
these temperature readings.
t(min)
Temp.
t(min)
Temp.
0
186
9
156
1
182
10
153
2
178
11
152
3
175
12
148
4
171
13
145
5
168
14
143
6
165
15
141
7
162
8
159
Based on your knowledge of cooling curves how far down do you expect the
temperature to drop?
It is necessary to reflect the fact that the temperature of the coffee only drops to
room temperature (70 degrees). We must first begin by subtracting 70 from each
of the temperatures.
t(min)
Temp.
t(min)
Temp.
0
115
9
86
1
112
10
83
2
108
11
81
3
105
12
78
4
101
13
75
5
98
14
73
6
95
15
71
7
92
Using your TI-83 calculator and the following directions input the data into List 1
and List 2.
 Each list needs to be cleared separately by following the following three
steps.
1. Press the Stat key and then the 4 key to get ClrList.
2. Complete the ClrList command by first selecting the List function
(above the Stat key) and then selecting the appropriate lists from the
menu. It is best to begin with all lists clear.
3. Press ENTER to clear the lists. The screen will display “DONE”
 Press the Stat key to reopen the Stat menu
 Press the 1 key to edit the lists.
 Using the arrow keys enter the time in L1 and the temperature in L2.
 Press the Stat key to get the Stat menu. Arrow over to highlight CALC.
Press 4 to get LinReg(ax+b). Press enter.
8
89
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Before viewing the graph you should set the window to an appropriate setting.
For this example the settings should be as follows:
o Xmin = 0
o Xmax = 15
o Xscl = 1
o Ymin = 70
o Ymax = 115
o Yscl = 2
o Xres = 1
Press the graph key to view your graph. At this point the graph is simply
plotted points. To connect these points with the line of best fit (regression
line) follow the remaining steps. Press the Y= key.
Clear any equations from this screen by using the Clear key.
Next press the VARS key.
Press 5 for Statistics.
Arrow over to highlight EQ and then press 1 for RegEQ.
The regression equation will then appear in the Y= screen.
Press the Graph screen and watch a line connect the points that you plotted
earlier.
Using the trace function you can trace the line and predict values that fall in
between those that you entered in the list screen.
Please draw a graph representing what your calculator displays after you have
completed these instructions.
What is the equation for the line of regression?
Questions:
1. At what time does the coffee reach the temperature 83.3244 degrees?
Use the trace function to approximate the time to five decimal places.
2. At t = 12.25 what is the temperature of the coffee? Use the Calc key
(located above the trace key) and select 1 for value. Please round to five
decimal places.
3. In the above experiment we assumed that the room temperature was kept
at a constant 70 degrees. In reality, we may assume that the temperature
of a room varies between a small range, for instance between 67 degrees
and 72 degrees due to the heating and cooling system of the building.
How might you take this variance into account in predicting the time the
cup of coffee will reach a certain temperature? How much of a difference
will the variance make?