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The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake, Io. M = log(f) Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake? O A. M = log(10,000) O B. (10,000 M = log(

The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake, Io. M = log(f) Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake? O A. M = log(10,000) O B. (10,000 M = log(

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
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 for Measuring Earthquake Magnitude** The Richter scale measures the magnitude, \( M \), of an earthquake as a function of its intensity, \( I \), and the intensity of a reference earthquake, \( I_0 \). The formula for this relationship is given by: \[ M = \log \left( \frac{I}{I_0} \right) \] ### Question: Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake? ### Options: - **A.** \( M = \log(10,000) \) - **B.** \( M = \log \left( \frac{10,000}{I_0} \right) \) - **C.** \( M = \log \left( \frac{I}{10,000} \right) \) - **D.** \( M = \log \left( \frac{1}{10,000} \right) \) ### Explanation: The correct answer should follow the form \( M = \log \left( \frac{I}{I_0} \right) \). Given that the intensity \( I \) of the earthquake is 10,000 times that of the reference intensity \( I_0 \), it can be expressed as \( I = 10,000 I_0 \). Substituting this into the formula, we get: \[ M = \log \left( \frac{10,000 I_0}{I_0} \right) = \log(10,000) \] Therefore, the correct option is: - **A.** \( M = \log(10,000) \) Please click the "Reset" button to start over or the "Next" button to proceed.
Transcribed Image Text:**Understanding the Richter Scale for Measuring Earthquake Magnitude** The Richter scale measures the magnitude, \( M \), of an earthquake as a function of its intensity, \( I \), and the intensity of a reference earthquake, \( I_0 \). The formula for this relationship is given by: \[ M = \log \left( \frac{I}{I_0} \right) \] ### Question: Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake? ### Options: - **A.** \( M = \log(10,000) \) - **B.** \( M = \log \left( \frac{10,000}{I_0} \right) \) - **C.** \( M = \log \left( \frac{I}{10,000} \right) \) - **D.** \( M = \log \left( \frac{1}{10,000} \right) \) ### Explanation: The correct answer should follow the form \( M = \log \left( \frac{I}{I_0} \right) \). Given that the intensity \( I \) of the earthquake is 10,000 times that of the reference intensity \( I_0 \), it can be expressed as \( I = 10,000 I_0 \). Substituting this into the formula, we get: \[ M = \log \left( \frac{10,000 I_0}{I_0} \right) = \log(10,000) \] Therefore, the correct option is: - **A.** \( M = \log(10,000) \) Please click the "Reset" button to start over or the "Next" button to proceed.
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