a. Find the earthquake intensity I in terms of the​ zero-level earthquake intensity Upper I 0.
b. Find the energy released by the earthquake.
Mequals5
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Part 1
a. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
​(Type your answer using exponential​ notation.)
A.
IequalsUpper I 0minus
  
enter your response here
B.
Iequals
  
10 Superscript 5Upper I 0
C.
IequalsStartFraction Upper I 0 Over nothing EndFraction
  
D.
IequalsUpper I 0plus
  
enter your response here
Part 2
b. The energy released by the earthquake of magnitude 5 is Eequals
  

​(Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to one decimal place as​ needed.)


### Part 1: Finding the earthquake intensity \( I \) in terms of the zero-level earthquake intensity \( I_0 \)

The relationship between the earthquake intensity \( I \) and its magnitude \( M \) is given by the formula:

\[
M = \log_{10} \left( \frac{I}{I_0} \right)
\]

Where:
- \( M \) is the magnitude of the earthquake.
- \( I \) is the intensity of the earthquake.
- \( I_0 \) is the zero-level earthquake intensity (reference intensity).

Given that \( M = 5 \), the equation becomes:

\[
5 = \log_{10} \left( \frac{I}{I_0} \right)
\]

To solve for \( I \), we raise both sides of the equation to the power of 10:

\[
10^5 = \frac{I}{I_0}
\]

This gives us:

\[
I = 10^5 I_0
\]

Thus, the correct answer for part (a) is:

\[
\boxed{I = 10^5 I_0}
\]

### Part 2: Finding the energy released by the earthquake

The energy released by an earthquake is related to its magnitude \( M \). The energy \( E \) is given by the formula:

\[
E = E_0 \times 10^{1.5M}
\]

Where:
- \( E_0 \) is a reference energy.
- \( M = 5 \) is the magnitude of the earthquake.

Substituting \( M = 5 \) into the formula:

\[
E = E_0 \times 10^{1.5 \times 5}
\]

\[
E = E_0 \times 10^{7.5}
\]

Thus, the energy released by the earthquake is proportional to \( 10^{7.5} \) times the reference energy \( E_0 \). If we assume \( E_0 \) represents the energy released by a zero-level earthquake, the value would depend on \( E_0 \), but the formula for the energy is:

\[
E = E_0 \times 10^{7.5}
\]

This can be written as \( E = E_0 \times 3.16 \times 10^7 \) (where \( 10^{7.5} \approx 3.16 \times 10^7 \)).

Would you like further details or have any questions?

### 5 Related Questions:
1. How does the Richter scale relate to earthquake magnitude and intensity?
2. How do different magnitudes affect the energy released in an earthquake?
3. What is the difference between earthquake magnitude and intensity?
4. Can the energy formula be used to compare two earthquakes with different magnitudes?
5. How is the zero-level earthquake intensity \( I_0 \) determined?

### Tip:
Magnitude increases by 1 unit on the Richter scale represent roughly a 32-fold increase in energy release.

a. Find the earthquake intensity I in terms of the zero-level earthquake intensity I_0. b. Find the energy released by the earthquake when magnitude M = 5.

Learn how to calculate the earthquake intensity in terms of zero-level intensity using logarithmic equations. Solve for the energy released by a magnitude 5 earthquake using exponential growth. Suitable for high school students learning logarithmic functions and the Richter scale.

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