**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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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(

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 2ECP: The number of bacteria in a culture is increasing according to the law of exponential growth. After...

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Question

**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) $

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