|APPLICATIONS OF EXPONENTIAL|
EARTHQUAKE WORD PROBLEMS:
As with any word problem, the trick is convert a narrative statement or question to a mathematical statement.
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
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 times strong than an earthquake of magnitude 5. An earthquake of magnitude 8 is times stronger than an earthquake of magnitude 5.
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Convert the ''The 1976 Tangshan earthquake was 1.26 as intense.'' to an equivalent mathematical equation.
where IMexico is the intensity of the Mexico City earthquake and ITangshon is the intensity of the Tangshon earthquake.
We are trying to determine the magnitude of the Tangshon earthquake.
Let's check our answer:
Convert both of these equations to exponential equations.
What you are looking for is the ratio of the intensities: ML-MS. So our task is to isolate this expression from the above given information using the rules of logarithms.
The difference between the magnitudes of the two earthquakes is 2.11 on the Richter scale.
Let's check the answer.
It will not check exactly because we rounded the 2.11, but it is sufficiently close to check our answer.
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