- Japan Earthquake Investigation Project -
-Pre-Calculus 3rd Qtr-
Name:_________________________________________
Date: _________________ Period: _____________
Projects are due absolutely no later than end of class (2B) on Wednesday, March 23,
2011. All work is to be students’ original thoughts and processes, neatly recorded
and attached to this project sheet. Incomplete assignments will not be accepted.
Topic: Recent Earthquake/Tsunami in Japan
Project: Using logarithms of a common base, further analyze magnitude of
earthquake in Japan and compare to catastrophic earthquake in Haiti from last year.
Background information:
Before we start, let's talk about earthquakes and how we measure their intensity.
In 1935 Charles Richter defined the magnitude of an earthquake to be
where I is the intensity of the earthquake (measured by the amplitude of a
seismograph reading taken 100 km from the epicenter of the earthquake) and S is
the intensity of a ''standard earthquake'' (whose amplitude is 1 micron =10-4 cm).
The magnitude of a standard earthquake is
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.
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: 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 American?
Solution: Convert the first sentence to an equivalent mathematical sentence or
equation.
Convert the second sentence to an equivalent mathematical sentence or equation.
Solve for MSA.
The intensity of the earthquake in South America was 8.9 on the Richter scale.
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Example 2: 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 1?
Solution: The intensity (I) of each earthquake was different. Let I1 represent the
intensity the early earthquake and I2represent the latest earthquake.
What you are looking for is the ratio of the intensities:
So our task is to isolate
this ratio from the above given information using the rules of logarithms.
Convert the logarithmic equation to an exponential equation.
The early earthquake was 16 times as intense as the later earthquake.
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Question 1 (5 pts): While a magnitude of 8.9 appears to be the official measure of
March 11, 2011 earthquake in Japan, other news sources have occasionally reported
a magnitude of 9.0. How many times more intense would the higher magnitude be
than the 8.9 measure?
Question 2 (5pts): The catastrophic earthquake in Haiti of January, 2010 was
measured as having a magnitude of 7.0. How many times more intense was the
earthquake in Japan? (Use a magnitude of 8.9.)
Question 3 (5 pts): On March 9, 2011, Japan experienced a sizeable precursor
tremble, known as a foreshock, now, to the ‘Big One’ that struck March 11. The ‘Big
One’ on March 11 was a magnitude of 8.9 and 79 times more intense than the
foreshock on March 9. What was the magnitude of the trembler from the 9th?
Additional Resources and Follow-up:
 A time-lapse of the tremors in Japan before and after the March 11
catastrophe: http://news.discovery.com/earth/time-lapse-animationshows-japans-earthquakes-110315.html

As you may have heard, the affects of the earthquake on Japan’s nuclearpowered energy systems has become a problem. In class, we discussed
exponential growth and decay. A good example of exponential decay is
radioactive material because their decay is measured in half-lifes. Food for
thought: If there is radiation detected in the evacuated areas, how long
before residents can return? Can you find information on the half-life of
these radioactive materials? A great resource is Radiation By the Numbers:
Isotopes To Watch, may be accessed at:
http://www.npr.org/blogs/health/2011/03/16/134567288/radiation-bythe-numbers-isotopes-to-watch?ps=sh_sthdl
Please follow up this assignment with a 2-3 sentence, thoughtful write-up
discussing your thoughts on what you have learned while working out the
earthquake magnitude problems AND from your own investigation into the current
crises in Japan (5 pts).