Precalculus: Graphs and Models, A Unit Circle Approach Chapter 3 -- Data Set Exercises

Data Set Exercises The following problems will ask you to enter data into a grapher, fit regression equations to the data, and answer related questions. The topics include linear, quadratic, cubic, quartic, logarithmic, logistic, and exponential modeling.

Section 3.1: Polynomial Functions and Modeling

1)	The following data represents the dry weight (in grams) of chick embryos of ages 6 to 16 days.

Days	Dry Weight
6	0.029
7	0.052
8	0.079
9	0.125
10	0.181
11	0.261
12	0.425
13	0.738
14	1.130
15	1.882
16	2.812

Source: Donald Burrill, Educational Psychologist

	a)	Enter the data and make a scatterplot using a grapher (use ZoomStat to view).
	b)	Use a grapher to fit quadratic, cubic, and quartic equations to the data. By comparing the values of R2, determine which equation best fits the data.

2) The table below represents the length and width of a sample of alligators.

Length (Inches)	Weight (Pounds)
94	130
74	51
147	640
58	28
86	80
94	110
63	33
86	90
69	36
72	38
128	366
85	84
82	80
86	83
88	70
72	61
74	54
61	44
90	106
89	84
68	39
76	42
114	197
90	102
78	57

Source: A.P. Statistics Teacher Handbook,
College Board

a) Enter the data and make a scatterplot using a grapher (use ZoomStat to view).

b) Use a grapher to determine whether a quadratic, cubic, or quartic function best fits the data by comparing R2 values.

c) Using the function from part b that best fits, predict the weight of an alligator that is 95 inches long.

3) The following data is the average price of a gallon of gasoline at a small midwestern gas station observed during a recent spring and summer.

Week Number	Price
1	1.20
2	1.31
3	1.43
4	1.67
5	1.80
6	1.82
7	1.85
8	1.87
9	2.01
10	1.84
11	1.68
12	1.52
11	1.68
12	1.52
13	1.44
14	1.30
15	1.27
16	1.21
17	1.26
18	1.29
19	1.32
20	1.35
21	1.38
22	1.42
23	1.48
24	1.50

	a)	Enter the data and make a scatterplot using a grapher (use ZoomStat to view).
	b)	Use a grapher to determine whether a cubic or quartic function best fits this data by comparing the value of R2.
	c)	Use this function to estimate what the price was in week 26.

Length (Inches)	Weight (Pounds)
94	130
74	51
147	640
58	28
86	80
94	110
63	33
86	90
69	36
72	38
128	366
85	84
82	80
86	83
88	70
72	61
74	54
61	44
90	106
89	84
68	39
76	42
114	197
90	102
78	57

	a)	Enter the data and make a scatterplot using a grapher (use ZoomStat to view).
	b)	Use a grapher to determine whether a quadratic, cubic, or quartic function best fits the data by comparing R2 values.
	c)	Using the function from part b that best fits, predict the weight of an alligator that is 95 inches long.

Length (Inches)	Weight (Pounds)
94	130
74	51
147	640
58	28
86	80
94	110
63	33
86	90
69	36
72	38
128	366
85	84
82	80
86	83
88	70
72	61
74	54
61	44
90	106
89	84
68	39
76	42
114	197
90	102
78	57

Length (Inches)	Weight (Pounds)
94	130
74	51
147	640
58	28
86	80
94	110
63	33
86	90
69	36
72	38
128	366
85	84
82	80
86	83
88	70
72	61
74	54
61	44
90	106
89	84
68	39
76	42
114	197
90	102
78	57