Using Logarithms to Determine Relationships

This unit from the Continuing Mathematics Project goes into detail on how logarithms can be used to determine the laws which connect two variables on which experimental data has been collected. The unit follows naturally from the unit entitled The Theory of Logarithms.

The objectives of the unit are that students:
(i) understand the meanings of the terms exponential growth and decay, as they are used in relation to natural phenomena;
(ii) perceive that money invested at 'compound interest' also grows exponentially in denominational terms (even if it decays exponentially in purchasing power);
(iii) be able, when the relationship between two variables x and y is of the form y = C.a^x, to plot values of log y against values of x on ordinary graph paper, or to plot values of y against values of x on log-linear graph paper, and so determine the constants C and a;
(iv) be able, when the relationship between two variables x and y is of the form y = C.x^a , to plot values of log y against values of log x on ordinary graph paper, or to plot the values of y against the values of x on log-log graph paper, and so determine C and a.

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