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A Powerful Function

A Powerful Function

    In the year of 1938, there was a Caltech seismologist, by the name of C.F. Richter, who had come up with an equation to define the magnitude of an earthquake. The equation went like this: 10^m = A/A o The letter “A” being the amplitude of the resulting shockwave measured in millimeters on a seismograph and “A o” is a constant that depends on the seismograph and how far it is from the location of the earthquake. In measuring earthquakes, one does not solve for “y” in terms of “x”, but to solve it for “x”. The problem of the taskset was to find a function that expresses “x” in terms of “y” when y= a^x.
    In order to accomplish this mathematical problem, one had to apply different mathematical concepts.This taskset revolved itself around the idea of exponential functions (y= ab^x). The use of logarithms and antilog also played an important role. There was also some calculation of ratios between logs and plotting data on graphs. This taskset also made use of composition of functions and a small portion of inverse functions. All this put together introduced the class to logarithms and their importance.

Square Craft Design

    The Museum of American Folk Art (somewhere in America) has decided to add a new section to their museum. They have hired a tilemaker to take a specific triangular pattern ,taken from an American quilt, and create a form of tile that can be used for both the floor and walls of the new section. The tilemaker is also responsible for creating a large tile as a centerpiece for the floor of the lobby. As a form of advertisement, the museum has agreed to create different projects such as t-shirts, posters, key chains, etc. using different sizes of the same triangular pattern. I, as a student, have been hired to find a form of determining the dimensions of the individual triangular components as a function of the size of the outer square.
    There are many d

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