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Unformatted text preview: ttention to the subtle differences. 6.1 Introduction to Exponential and Logarithmic Functions 343 (a) Earthquakes are complicated events and it is not our intent to provide a complete discussion of the science involved in them. Instead, we refer the interested reader to a solid course in Geology10 or the U.S. Geological Survey’s Earthquake Hazards Program found here and present only 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 x M (x) = log 0.001 where x is the seismograph reading in millimeters of the earthquake recorded 100 kilometers from the epicenter. i. Show that M (0.001) = 0. ii. Compute M (80, 000). iii. Show that a...
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