Logarithmic function can be found in psychology as well. An example of logarithmic function is the curve of forgetting which is represented by the graph of the following function: f(t) = A – B log(t+1), with A and B being experimentally determined constants. The parameter t is time that has lapsed from the moment we have learned something, expressed in months, and f(t) is the result of a test that measures your knowledge, expressed in percentage terms.
When they tested some students’ knowledge of mathematics at the end of the school year and a few times after that, they got the following function: f(t) = 78 – 15log(t+1).
a.) Draw the graph of the function (you will probably have to set the appropriate size of the units).
b.) What was the average result of the first test (at the end of the school year)? . . . . . . . . . . . .
What was the result after 4 months? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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c.) Does the following question make any sense: How long does it take for the students to know nothing (or even less than nothing)? Substantiate!
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Regardless of your answer to the above question, calculate when total loss of knowledge would occur:
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