Here is a student favorite:

Below is a set of data for a 1986 Peavy Patriot electric guitar. The data measure the distance in centimeters from the guitar frets to the bridge of the guitar.

Note: Fret 0 is an open string.

Fret #
0
1
2
3
4
5
6
7
8
9
10
11
Distance
63.5
59.8
56.4
53.3
50.3
47.5
44.9
42.5
40.1
37.9
35.7
33.8



12
13
14
15
16
17
18
19
20
21
22
23
31.9
30.2
28.5
26.9
25.4
24.1
22.7
21.4
20.3
19.2
18.1
17.1



The Raw Data
Distance vs. Fret #
The Transformed Data
ln(Distance) vs. Fret #
ln(D)=-.0569*F+4.1467
The Final Fitted Data
y=63.2243*.9447^X

The original data is clearly patterned. Perhaps it is an exponential relationship.

The semi-log plot "straightens" the data. The equation for the line can be obtained using the statistics options on the calculator.

The original data and the equation modeling that data can be displayed simultaneously.

When the data are properly fit using the ln(x) transformations, the discussion can begin about why the resulting exponential equation looks the way it does.

Most students are very surprised about the importance of the inverse of the twelfth root of 2.

Additionally, convenient data sharing with your class, for an examples similar to this one, is discussed in the workshops.