For the each data table below determine the function that describes the relationship between the two variables by linearizing the data table. For each data table this means:

All of the steps are shown in the YouTube video on the linearization,http://youtu.be/wgSEmMP-eQk. -This is the same video from Page 6 of this section. You don't need to watch it twice.)

 

Here is a typed list of the steps, mentioned in the video above, to linearizing your data.

  1. To find Logger Pro on Your windows 7 or 8 computer, press the "windows" button until you see the tiles. Then type, "Logger," and select "LoggerPro."
  2. Start a new "Logger Pro" document. To launch "Logger Pro," press the windows button and begin to type, "Logger." Then select "Logger Pro" from the list that pops up on the right.
  3. Enter the data into LoggerPro. You might want to press the "A" icon after entering the data to "Auto-Scale" the graph.
  4. Use the shape and your brain to match the graph up to one of the 5 types of graphs.
  5. Perform the function you've determined to the "x" values. (For example if you've determined that the graph represents an square root function, then square root all the "x" data in a calculated column in Logger Pro.
  6. Plot these values, from the newly created calculated column, on a graph. (See the video above.)
  7. Using the statistics button, determine the line's slope, y-intercept, and RMSE. (If the RMSE is too big, try a different function and go back to step 4.)
  8. Create your final science equation. (You will need to make up a variable for the concept listed. Just pick a letter that makes sense.)
  9. Save the document onto your computer. Start a new Logger Pro document for each data table.
  10. When working with a group, move your LoggerPro file to the shared lab folder on the Google Drive.
  A.

The displacement is the independent variable.

Displacement
(m)

Force
(N)
1 0
2 9
3 24
4 45
5 72
6 105
7 144
8 189
9 240
10 297
Do the problem and then use the answer below to check your work.

VIDEO SOLUTION: http://youtu.be/7voPemvgDSQ?list=UU4HomD6leEUKOiIC4jM5P2w

  B.

The volume is the independent variable.

Volume (dB) Distance (m)
0.11 1
0.25 1.5
0.44 2
0.69 2.5
1.00 3
1.36 3.5
1.78 4
2.25 4.5
2.78 5
3.36 5.5
  C.

The "C-field" is the independent variable.

C-field (Wa) Time (s)
0.043 50
0.049 45
0.056 40
0.065 35
0.077 30
0.095 25
0.125 20
0.182 15
0.333 10
2.000 5
  D.

Time is the independent variable.

time
(s)

displacement (m)
.1 0.03
.2 0.12
.5 0.75
1 3
2 12
3 27
4 48

5

75

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)