In 1949, Washington was struck by a 7.1 magnitude earthquake on the Richter scale. It has been predicted that Washingt is due for a 9.0 magnitude quake. Using the Richter scale equation above, determine how many times more forceful the predicted earthquake would be, compared to the 1949 quake.
In 1949, Washington was struck by a 7.1 magnitude earthquake on the Richter scale. It has been predicted that Washingt is due for a 9.0 magnitude quake. Using the Richter scale equation above, determine how many times more forceful the predicted earthquake would be, compared to the 1949 quake.
Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Understanding the Richter Scale and Earthquake Magnitude**
**Level 4: Advanced**
The Richter scale is utilized to describe the magnitude of earthquakes. The following equation represents how geologists calculate the Richter scale magnitude:
\[ \log (x) = \text{Richter scale} \]
where \( x \) represents the amount of force produced by the earthquake.
**Example Calculation**
In 1949, Washington was struck by a 7.1 magnitude earthquake on the Richter scale. It has been predicted that Washington is due for a 9.0 magnitude quake. Using the Richter scale equation above, determine how many times more forceful the predicted earthquake would be, compared to the 1949 quake.
**Solution Steps:**
1. **Convert Magnitudes to Force**
For the 7.1 magnitude earthquake:
\[ x_1 = 10^{7.1} \]
For the 9.0 magnitude earthquake:
\[ x_2 = 10^{9.0} \]
2. **Calculate the Ratio of the Forces**
\[ \frac{x_2}{x_1} = \frac{10^{9.0}}{10^{7.1}} = 10^{(9.0 - 7.1)} = 10^{1.9} \]
3. **Determine the Multiplicative Factor**
Using the value of \( 10^{1.9} \):
\[ 10^{1.9} \approx 79.43 \]
Thus, the predicted 9.0 magnitude earthquake would be approximately 79.43 times more forceful than the 7.1 magnitude earthquake that occurred in 1949.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F045a282d-b0cb-4622-ab73-b7a8c4ba053b%2F24a0c4cc-f30d-4a84-94aa-fff39d972349%2Fbwf1teu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Richter Scale and Earthquake Magnitude**
**Level 4: Advanced**
The Richter scale is utilized to describe the magnitude of earthquakes. The following equation represents how geologists calculate the Richter scale magnitude:
\[ \log (x) = \text{Richter scale} \]
where \( x \) represents the amount of force produced by the earthquake.
**Example Calculation**
In 1949, Washington was struck by a 7.1 magnitude earthquake on the Richter scale. It has been predicted that Washington is due for a 9.0 magnitude quake. Using the Richter scale equation above, determine how many times more forceful the predicted earthquake would be, compared to the 1949 quake.
**Solution Steps:**
1. **Convert Magnitudes to Force**
For the 7.1 magnitude earthquake:
\[ x_1 = 10^{7.1} \]
For the 9.0 magnitude earthquake:
\[ x_2 = 10^{9.0} \]
2. **Calculate the Ratio of the Forces**
\[ \frac{x_2}{x_1} = \frac{10^{9.0}}{10^{7.1}} = 10^{(9.0 - 7.1)} = 10^{1.9} \]
3. **Determine the Multiplicative Factor**
Using the value of \( 10^{1.9} \):
\[ 10^{1.9} \approx 79.43 \]
Thus, the predicted 9.0 magnitude earthquake would be approximately 79.43 times more forceful than the 7.1 magnitude earthquake that occurred in 1949.
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