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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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