Answer:
To determine the change in the Richter scale magnitude given an intensity, we can use the relationship between intensity and magnitude. The Richter scale measures the magnitude of an earthquake, while the intensity is often related to the perceived strength of shaking.
The intensity \( I \) of an earthquake can be related to its magnitude \( M \) on the Richter scale through the following empirical formula:
\[ I = 10^{1.5M} \]
Given the intensity \( I = 50 \), we can find the magnitude \( M \) by rearranging the formula:
\[ 50 = 10^{1.5M} \]
To solve for \( M \), take the logarithm of both sides:
\[ \log_{10}(50) = 1.5M \]
Now, calculate \( \log_{10}(50) \):
\[ \log_{10}(50) \approx 1.69897 \]
Then, solve for \( M \):
\[ 1.69897 = 1.5M \]
\[ M = \frac{1.69897}{1.5} \]
\[ M \approx 1.13265 \]
So, the magnitude \( M \) corresponding to an intensity of 50 on the Richter scale is approximately 1.13.
