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]