Seismologists compare the intensities of earthquakes using the formula $I = 10^R$, where $R$ represents the magnitude on the Richter scale. To compare the intensity of a magnitude 8.2 earthquake to a magnitude 5.1 earthquake, which mathematical ratio should be used?

An insurance risk analyst is comparing historical seismic events to model potential damage using the intensity formula $I = 10^R$. When comparing the 2014 Chile earthquake (magnitude 8.2) to the 2014 Los Angeles earthquake (magnitude 5.1), the ratio of their intensities simplifies to ${}10^{3.1}$. This means the Chile earthquake was approximately ____ times as intense as the Los Angeles earthquake.

A public safety officer is preparing a report to compare the 2014 Chile earthquake (magnitude 8.2) and the 2014 Los Angeles earthquake (magnitude 5.1). Arrange the steps the officer should follow to determine how many times more intense the Chile earthquake was using the intensity formula $I = 10^R$.

A seismic risk analyst for an insurance company is organizing data from 2014 earthquakes for a safety report. Match each seismic detail from the 2014 Chile and Los Angeles events with its correct mathematical representation using the intensity formula $I = 10^R$.

Simplifying Earthquake Intensity Ratios