|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 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.
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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