Nonlinear Transformations
Name_____________________
1. The table below gives the age (in years) and the diameter (in inches) for twenty-seven oak
trees. Find a linear transformation to describe this and then predict the diameter for a
tree that is 24 years old. (Data continues over to the right)
Age
4
5
8
8
8
10
10
12
13
14
16
18
20
22
Diameter
0.8
0.8
1
2
3
2
3.5
4.9
3.5
2.5
4.5
4.6
5.5
5.8
Age
23
25
28
29
30
30
33
34
35
38
38
40
42
Diameter
4.7
6.5
6
4.5
6
7
8
6.5
7
5
7
7.5
7.5
2. The following represents data about lead content. Let x = the distance away from a highway
and y = the lead content of the soil at that point. Find the best linear transformation and
then use it to predict the lead content for a distance of 18 miles.
x
0.3
1
5
10
15
20
25
30
40
50
75
100
y
62.75
37.51
29.7
20.71
17.65
15.41
14.15
13.5
12.11
11.4
10.85
10.85