The table gives the loudness of spoken words, measured at the source, and the maximum distance at which another person can recognize the speech. Find an equation that expresses the maximum distance as a function of loudness.
a. Plot the data on your calculator and make a rough sketch on your paper.
b. Experiment to find the relationship between x and y by plotting different combinations of x, y, log x, and log y until you have found the graph that best linearizes the data. Sketch this graph on your paper and label the axes with x, y, log x, or log y, as appropriate.
c. Find the equation of a line that fits the plot you chose in 7b.
Remember that your axes did not represent x and y, so substitute (log x) or (log y) into your equation as appropriate.
d. Graph this new equation with the original data. Does it seem to be a good model?
Loudness (dB) Distance (m)
0.5................................0.1
3.2................................16.0
5.3................................20.4
16.8..............................30.5
35.8..............................37.0
84.2..............................44.5
120.0.............................47.6
170.0.............................50.6