Question

On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?

M=log (I/I₀)

M= the magnitude of an earthquake
I= the intensity of an earthquake
I₀= the smallest seismic activity that can be measured, which is 1
a. 0.40
b. 1.02
c. 1.05
d. 2.51

Answer 1

Using the logarithmic scale for earthquake magnitudes, the first earthquake's intensity was approximately 2.51 times greater than the second earthquake's intensity, based on their respective magnitudes of 8.6 and 8.2. the correct option is (d).

Step-by-step explanation:

The intensity of an earthquake can be approximated by using the formula I = 10^(1.5M), where M is the magnitude of the earthquake. In this case, the first earthquake had a magnitude of 8.6 and the second earthquake had a magnitude of 8.2. We can calculate the intensity of each earthquake using the formula.

For the first earthquake:

I = 10^(1.5*8.6) = 10^12.9

For the second earthquake:

I = 10^(1.5*8.2) = 10^12.3

To find the approximate factor by which the intensity of the first earthquake was greater than the second earthquake, we can divide the intensity of the first earthquake by the intensity of the second earthquake.

Factor = (10^12.9) / (10^12.3) = 10^(12.9 - 12.3) = 10^0.6 ≈ 2.51

Therefore, the approximate factor by which the intensity of the first earthquake was greater than the second earthquake is 2.51.