Algebra
GRAPHING
data, it is called an extrapolated value. Although the value of 0.956 g/ml appears reasonable, an
important physical fact is absent and not predictable from the data given. Water boils at 100°C
at atmospheric pressure. At temperatures above 100°C it is not a liquid, but a gas. Therefore,
the value of 0.956 g/ml is of no significance except when the pressure is above atmospheric.
This illustrates the relative ease of interpolating and extrapolating using graphs. It also points
out the precautions that must be taken, namely, interpolation and extrapolation should be done
only if there is some prior knowledge of the system. This is particularly true for extrapolation
where the available data is being extended into a region where unknown physical changes may
take place.
Logarithmic 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.
TABLE 1
Data on the Radioactive Decay of Strontium 90
Time (years)
Amount of Strontium 90 (grams)
0
100
25
50
50
25
75
12.5
100
6.25
125
3.125
150
1.5625
175
0.78125
Rev. 0
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MA-02
