![]() To do so, we take the original data set (the columns "time" and "proportion") and find the logarithm of the independent variable, time. We know from the section on Graphs on Logarithmic and Semi-Logarithmic Axes that we can turn a logarithmic (or exponential) curve into a linear curve by taking the logarithm of one of the variables. We now aim to find the values of c and d. We assume our logarithmic function will have the form: The answer: We observe it is most like Figure 5, which had the formula y = −log 10( x). The question: You can see a "best fit" curve has been drawn through the data points. (This is the famous Ebbinghaus Forgetting Curve.) The average data is plotted over time as follows, where the horizontal axis is time, and the vertical axis is the proportion of the words they got right. As expected, the number of words they remember correctly diminishes over time. They are tested immediately, then again after some time has elapsed, and then repeatedly over longer time spans. The experiment: A group of people are asked to learn a list of random words. But for the sake of explaining how to determine an unknown logarithmic function from its data plot, let's take a look at this example (one which is close to my heart). There are many computer packages (SPSS, Excel, etc) that can determine a "best fit" curve for a given set of data. Determining the equation of a logarithmic function from data We know the graph needs to pass through (−1, 0), and we observe we are 1.5 units too high. Example 6a: Interim graph, moved 2.5 units left
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