AlgebraGRAPHINGdata, it is called an extrapolated value. Although the value of 0.956 g/ml appears reasonable, animportant physical fact is absent and not predictable from the data given. Water boils at 100°Cat 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 pointsout the precautions that must be taken, namely, interpolation and extrapolation should be doneonly if there is some prior knowledge of the system. This is particularly true for extrapolationwhere the available data is being extended into a region where unknown physical changes maytake place.LogarithmicGraphsFrequently, the function to be plotted on a graph makes it convenient to use scales different fromthose used for the Cartesian coordinate graphs. Logarithmic graphs in which one or both of thescales are divided logarithmically are common. A semi-log plot is used when the function is anexponential, such as radioactive decay. A semi-log plot is obtained by using an ordinary linearscale for one axis and a logarithmic scale for the other axis. A log-log plot is used when thefunction is a power. A log-log plot is obtained by using logarithmic scales for both axes. Table1 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 graphof the data given in Table 1. It can be seen from Figure 4 that it is difficult to determine fromthis plot the amount of strontium 90 present after long periods of time such as 125 years, 150years, or 175 years.TABLE 1Data on the Radioactive Decay of Strontium 90Time(years)AmountofStrontium90(grams)0 10025 5050 2575 12.5100 6.25125 3.125150 1.5625175 0.78125Rev. 0 Page 77 MA-02
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