Algebra III/Trig
January 2016
Logarithmic applications
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I
where I is the intensity of the
I0
earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicenter of the
earthquake) and I 0 is the intensity of a ''standard earthquake'' (whose amplitude is 1.5 x 10-5 in. of ground
movement). Richter studied many earthquakes that occurred between 1900 and 1950. The largest had
magnitude of 8.9 on the Richter scale, and the smallest had magnitude 0. This corresponds to a ratio of
intensities of 800,000,000, so the Richter scale provides more manageable numbers to work with.
In 1935 Charles Richter defined the magnitude of an earthquake to be R  log
Each number increase on the Richter scale indicates an intensity ten times stronger. For example, an earthquake
of magnitude 6 is ten times stronger than an earthquake of magnitude 5. An earthquake of magnitude 7 is
10 x 10 = 100 times strong than an earthquake of magnitude 5. An earthquake of magnitude 8 is
10 x 10 x 10 = 1000 times stronger than an earthquake of magnitude 5.
Example 1: If the intensity of an elephant walking is 5.97 x 10-4, find the magnitude of each step.
Example 2: If a large hand grenade has the intensity of 2.38 x 10-5, find the magnitude of the blast.
Example 3: If the Richter scale measures a small construction blast at a 1, what is the intensity of ground
movement caused by the blast?
Example 4: If the Richter scale measured the explosion at Chernobyl nuclear power plant in 1986 at a 3.74,
what was the intensity of ground movement caused by the explosion?
Example 5: Early in the century the earthquake in San Francisco registered 8.3 on the Richter scale. In the
same year, another earthquake was recorded in South America that was four time stronger. What was the
magnitude of the earthquake in South America?
Example 6: A recent earthquake in San Francisco measured 7.1 on the Richter scale. How many times more
intense was the San Francisco earthquake described in Example 5 ?
Example 7: How much more intense is an earthquake of magnitude 6.5 on the Richter scale as one with a
magnitude of 4.9?
Example 8: If one earthquake is 25 times as intense as another, how much larger is its magnitude on the Richter
scale?