Y 03476t 2 10253t 04771 r² 09699 0 10 20 30 40 50 60

y = -0.3476t 2 + 10.253t -0.4771
R² = 0.9699
0
10
20
30
40
50
60
70
80
0 4 8 12 16 20 24
Temperature (degrees)
Time of Day (hour)
Temperature
on a Spring Day

(c) Use the quadratic polynomial
y = - 0.3476 t
2
+ 10.253 t - 0.4771
together with algebra to estimate the time(s) of
day when the outdoor temperature
y
was 62 degrees.
That is, solve the quadratic equation
62 = - 0.3476 t
2
+ 10.253 t - 0.4771
Show algebraic work in solving. State your results clearly; report the time(s) to the nearest quarter hour.
.
10. (10 pts) + (extra credit at the end) EXPONENTIAL REGRESSION [Section 6.5]
Data: A cup of hot coffee was placed in a room maintained at a constant temperature of 69 degrees, and the
coffee temperature was recorded periodically, in Table 1.
TABLE 1
t = Time
Elapsed
(minutes)
C = Coffee
Temperature
(degrees F.)
0 166.0
10 140.5
20 125.2
30 110.3
40 104.5
50 98.4
60 93.9
REMARKS:
Common sense tells us that the coffee will be cooling off
and its temperature will decrease and approach the ambient
temperature of the room, 69 degrees.
So, the temperature difference between the coffee
temperature and the room temperature will decrease to 0.
We will fit the temperature difference data (Table 2) to an
exponential curve of the form
y = A e
- bt
.
Notice that as t gets large, y will get closer and closer to 0,
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

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 70 minutes have elapsed. Report
your estimated temperature difference to the nearest tenth of a degree.
(explanation/work optional)