As a risk assessment analyst for an insurance firm, you are tasked with comparing historical seismic events to update property damage models. To begin comparing two earthquakes, you must convert their given magnitudes ($R$) into intensities ($I$). Based on standard earthquake models, which of the following formulas correctly represents this conversion?

A seismic analyst for a city government is preparing a report comparing the 1906 San Francisco earthquake (magnitude 7.8) and the 1989 Loma Prieta earthquake (magnitude 6.9). Arrange the steps below in the correct mathematical order to determine how many times more intense the 1906 earthquake was compared to the 1989 earthquake.

As a trainee in an emergency management office, you are reviewing historical data for the 1906 San Francisco earthquake (magnitude 7.8) and the 1989 Loma Prieta earthquake (magnitude 6.9). Using the intensity model $I = {}10^R$, match each description with its corresponding numerical value or mathematical expression used to compare these two events.

In a seismic safety report comparing two historical events, the 1906 San Francisco earthquake (magnitude 7.8) is found to be approximately ____ times as intense as the 1989 Loma Prieta earthquake (magnitude 6.9) when using the model $I = {}10^R$.

According to the seismic intensity model $I = 10^R$, the ratio of intensities between the 1906 San Francisco earthquake (magnitude {}7.8) and the 1989 Loma Prieta earthquake (magnitude {}6.9) is correctly represented by the expression ${}10^{7.8 - 6.9}$.

Comparing Earthquake Intensities in Public Safety Fact Sheets

Documenting Historical Seismic Intensity Comparisons