Part I
Reproduce the results in Examples 1 – 6.
Part II
Work the assigned problems.
[7] The water temperature at a faucet was measured (on the Fahrenheit temperature scale) each second after the hotwater tap is turned on. The results were: 72° at 1 second, 72° at 2 seconds, 75° at 3 seconds, 82° at 4 seconds, 95° at 5 seconds, 103° at 6 seconds, 105° at 7 seconds, and 105° at 8 seconds.
 What type of model is appropriate for this situation?
 At what time is the temperature changing most rapidly?
 About how fast is the temperature changing when it changes fastest?
[8] The weight of babies at birth to the nearest pound is tabulated from birth records, with these results: 1% weigh 2 pounds or less, 1% weigh 3 pounds, 2% weigh 4 pounds, 5% weigh 5 pounds, 19% weigh 6 pounds, 36% weigh 7 pounds, 26% weigh 8 pounds, 8% weigh 9 pounds, 1% weigh 10 pounds or more. If a normaldistribution model is fit to this data, what is the bestfit value for the width parameter?
[9] A bank balance earning a constant rate of compound interest has these values: $1550 after 5 years, $2002 after 10 years, $2585 after 15 years, $3339 after 20 years, and $4313 after 25 years. Find a model formula to compute how long it took for the balance to equal $2,938.
[10] Because the earth’s orbit around the sun is an ellipse, the distance between them varies according to the time of year. The table to the right shows the distance in miles at 50day intervals (the first data point is the 50th day of the year, February 19th). Fit a sinusoidal model to this data, and then use the parameters of the model to compute the closest distance that occurs.
Day 
Distance 
50 
91,907,193 
100 
93,146,982 
150 
94,243,003 
200 
94,460,990 
250 
93,660,185 
300 
92,366,382 
350 
91,477,551 
Problems 11–20 have the same instructions, applied to different datasets. Copy and paste the datasets from the course web site copy of this topic into a spreadsheet, rather than retyping them.
For each of the datasets listed below (copy and paste it from the course website and)
 Display the dataset and determine which model type discussed in this course is most suitable.
 Write the bestfit formula that shows how to compute the y values from the x values.
[11] Dataset A
x 
y 
1 
26.52 
2 
26.41 
3 
26.12 
4 
25.43 
5 
23.91 
6 
21.05 
7 
17.03 
8 
13.16 
9 
10.60 
10 
9.29 
11 
8.70 
12 
8.46 
13 
8.37 
14 
8.33 
15 
8.31 
16 
8.30 

[12] Dataset B
x 
y 
0 
172 
1 
195 
2 
216 
3 
230 
4 
244 
5 
256 
6 
261 
7 
266 
8 
264 
9 
262 
10 
255 
11 
247 

[13] Dataset C
x 
y 
0 
66.8 
2 
65.3 
4 
64.2 
6 
63.6 
8 
63.6 
10 
64.2 
12 
65.4 
14 
66.9 
16 
68.4 
18 
69.7 
20 
70.6 
22 
70.9 
24 
70.5 
26 
69.6 
28 
68.2 
30 
66.7 

[14] Dataset D
x 
y 
1 
239.7 
2 
296.6 
3 
386.6 
4 
469.9 
5 
597.6 
6 
777.3 
7 
952.2 
8 
1180.0 
9 
1424.4 
10 
1682.6 
11 
1980.3 
12 
2309.7 

[15] Dataset E
x 
y 
1992 
45,619 
1993 
49,529 
1994 
53,405 
1995 
57,228 
1996 
60,877 
1997 
65,003 
1998 
68,849 
1999 
72,399 
2000 
76,529 
2001 
80,448 
2002 
84,030 
2003 
88,027 

[16] Dataset F
x 
y 
1991 
0.5% 
1992 
1.1% 
1993 
2.2% 
1994 
4.5% 
1995 
8.8% 
1996 
16.5% 
1997 
28.9% 
1998 
45.5% 
1999 
63.2% 
2000 
77.9% 
2001 
87.9% 
2002 
93.7% 
2003 
96.8% 
2004 
98.4% 
2005 
99.2% 
2006 
99.6% 

[17] Dataset G
x 
y 
0 
10.65 
1 
8.46 
2 
7.10 
3 
5.60 
4 
4.74 
5 
3.90 
6 
3.09 
7 
2.62 
8 
2.00 
9 
1.55 
10 
1.47 
11 
0.98 
12 
0.76 
13 
0.97 
14 
0.62 
15 
0.49 
16 
0.42 
17 
0.29 
18 
0.27 
19 
0.21 
20 
0.20 

[18] Dataset H
x 
y 
0 
0.0% 
1 
0.1% 
2 
2.2% 
3 
15.0% 
4 
36.8% 
5 
33.3% 
6 
11.1% 
7 
1.4% 
8 
0.1% 
9 
0.0% 
10 
0.0% 
11 
0.0% 
12 
0.0% 

[19] Dataset I
x 
y 
0 
0.00 
10 
52.18 
20 
73.57 
30 
90.41 
40 
104.30 
50 
116.60 
60 
127.82 
70 
138.09 
80 
147.46 
90 
156.65 
100 
164.93 
110 
172.89 
120 
180.86 

[20] Dataset J
x 
y 
0 
0 
2 
0 
4 
2 
6 
4 
8 
9 
10 
17 
12 
32 
14 
48 
16 
61 
18 
67 
20 
69 
22 
62 
24 
48 
26 
33 
28 
19 
30 
11 
32 
5 
34 
2 
36 
1 
38 
0 
40 
0 
