The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density.
| | Land Area ($mi^2$) | Seismic Activity Density |
| :------ | :------------------ | :----------------------- |
| State A | 165696 | 0.0299 |
| State B | 10931 | 0.1402 |
Which statement about the number of earthquakes the states had for the given time span is true?
A. State A had approximately 1,533 more earthquakes than State B.
B. State B had approximately 1,533 more earthquakes than State A.
C. State A had approximately 3,362 more earthquakes than State B.
D. State B had approximately 3,362 more earthquakes than State A
Answer (2)
Calculate the number of earthquakes in State A: 165696 × 0.0299 = 4954.3104 .
Calculate the number of earthquakes in State B: 10931 × 0.1402 = 1532.5262 .
Find the difference: 4954.3104 − 1532.5262 = 3421.7842 .
State A had approximately 3,362 more earthquakes than State B. State A had approximately 3,362 more earthquakes than State B.
Explanation
Understanding the Problem We are given the land area and seismic activity density for two states, State A and State B. The seismic activity density is the ratio of the number of earthquakes to the land area. Our goal is to determine which statement about the difference in the number of earthquakes between the two states is true.
Calculating Earthquakes in Each State First, we need to calculate the number of earthquakes in each state. The number of earthquakes is the product of the land area and the seismic activity density.
Earthquakes in State A For State A, the number of earthquakes is: 165696 × 0.0299 = 4954.3104
Earthquakes in State B For State B, the number of earthquakes is: 10931 × 0.1402 = 1532.5262
Finding the Difference Now, we find the difference in the number of earthquakes between State A and State B: 4954.3104 − 1532.5262 = 3421.7842 Rounding to the nearest whole number, the difference is approximately 3422.
Conclusion Since the difference is positive, State A had more earthquakes than State B. The difference is approximately 3422 earthquakes. Therefore, State A had approximately 3,422 more earthquakes than State B. The closest option to this value is 3,362.
Examples
Understanding seismic activity is crucial for urban planning and disaster preparedness. For instance, knowing the seismic activity density of a region helps engineers design earthquake-resistant buildings. By analyzing the frequency and intensity of earthquakes in an area, urban planners can implement safety measures, such as evacuation routes and emergency response systems, to minimize the impact of seismic events on communities. This knowledge also aids in setting appropriate building codes and insurance rates, ensuring that structures can withstand potential earthquakes and that residents are adequately protected.
State A had approximately 3,362 more earthquakes than State B, based on the calculations from the provided land area and seismic activity density. The correct answer is option C. This information is essential for understanding regions with higher earthquake risks.
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