question archive Earthquakes are complicated events, and so the intent here is not to provide a complete discussion of the science involved in them

Earthquakes are complicated events, and so the intent here is not to provide a complete discussion of the science involved in them

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Earthquakes are complicated events, and so the intent here is not to provide a complete discussion of the science involved in them. Rather, we will look at a simplified version of the Richter scale. The Richter scale measures the magnitude of an earthquake by comparing the amplitude of the seismic waves of the given earthquake to those of a "magnitude 0 event", which was chosen to be a seismograph reading of 0.001 millimeters recorded on a seismometer 100 kilometers from the earthquake's epicenter. Specifically, the magnitude of an earthquake is given by: M(x) = log (x/0.001), where x is the seismograph reading in millimeters of the earthquake recorded 100 kilometers from the epicenter.

1) Use the formula for the magnitude of an earthquake and do the following:

a) Show that M(0.001) = 0.

b) Compute M(80,000).

c)  Show that an earthquake which registered 6.7 on the Richter scale had a seismograph reading ten times larger than one which measured 5.7.

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