Graphs

Frequently, the function to be plotted on a graph makes it convenient to use scales different from those used for the Cartesian coordinate graphs. Logarithmic graphs in which one or both of the scales are divided logarithmically are common. A semi-log plot is used when the function is an exponential, such as radioactive decay. A semi-log plot is obtained by using an ordinary linear scale for one axis and a logarithmic scale for the other axis. A log-log plot is used when the function is a power. A log-log plot is obtained by using logarithmic scales for both axes. Table 1 gives data on the amount of radioactive strontium 90 present as a function of time in years. Every twenty-five years one-half of the material decays. Figure 4 is a Cartesian coordinate graph of the data given in Table 1. It can be seen from Figure 4 that it is difficult to determine from this plot the amount of strontium 90 present after long periods of time such as 125 years, 150 years, or 175 years.

Figure 4 Cartesian Coordinate Plot of Radioactive Decay of Strontium 90

If the same data, the decay of strontium 90, is plotted on semi-log, the resulting plot (Figure 5) will be a straight line. This is because the decay of radioactive material is an exponential function. The resulting straight line of the semi-log plot allows a more accurate extrapolation or interpolation of the data than the curve obtained from the cartesian plot.

For graphs in which both of the quantities (x,y) vary as a power function, a log-log plot is convenient. A log-log plot is obtained by using logarithmic scales for both axes. Table 2 gives data on the frequency of electromagnetic radiation as a function of the wavelength of the radiation. Figure 6 is a log-log plot of the data given in Table 2.

Figure 5 Semi-log Plot of Radioactive Decay of Strontium 90

Figure 6 Log-Log Plot of Frequency vs. Wavelength of Electromagnetic Radiation

In summary, the type of coordinate system used to plot data, Cartesian, semi-log, or log-log, should be based on the type of function to be graphed and the desired shape (curve or line) of the curve wanted.

Cartesian system - Linear (y = mx + b) type functions when plotted will provide straight lines; exponential functions (y = eX) will plot as curves.

Semi-log system - Should not plot linear type functions on semi-log. Exponential functions, such as radioactive decay and reactor power equations when plotted will graph as straight lines.

Log-log - Rarely used; used to plot power equations.