Problem 8: Earthquake intensity is measured by the Richter scale. The formula for the Richter rating of a given quake is given by \( R=\log [1 \div 10] \) where 10 is the "threshold quake", or movement that can barely be detected, and the intensity \( l \) is given in terms of multiples of that threshold intensity.
You have a seismograph set up at home, and see that there was an event while you were out that had an intensity of \( \mathrm{I}=98910 \). Given that a heavy truck rumbling by can cause a microquake with a Richter rating of 3 or 3.5 , and "moderate" quakes have a Richter rating of 4 or more, what was likely the event that occurred while you were out?
Answer
Compare R to given Richter ratings: 3.995 > 3.5, 3.995 < 4
Step 1 ：Calculate R: R = log\( \frac{I}{10} \) = log\( \frac{98910}{10} \)
Step 2 ：Evaluate R: R = log\( 9891 \) \approx 3.995
Step 3 ：Compare R to given Richter ratings: 3.995 > 3.5, 3.995 < 4
