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The Los Angeles area experiences many earthquakes. In 1994, the Northridge earthquake measured 6.7 on the Richter scale. In 2014, Los Angeles experienced an earthquake that measured 5.1 on the Richter scale. Compare the intensities of the two earthquakes. Use a logarithmic model to solve. Round to the nearest whole number.

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Answer:

[tex]I_1=40I_2[/tex]

Step-by-step explanation:

[tex]M_1[/tex] = Magnitude of 1994 earthquake = 6.7

[tex]M_2[/tex] = Magnitude of 2014 earthquake = 5.1

[tex]I_1[/tex] = Intensity of 1994 earthquake

[tex]I_2[/tex] = Intensity of 2014 earthquake

[tex]I_0[/tex] = Zero-level earthquake the same distance from the epicenter = 0.001 mm

Magnitude is given by

[tex]M_1=\log(\dfrac{I_1}{I_0})\\\Rightarrow I_010^{M_1}=I_1\\\Rightarrow I_1=I_010^{6.7}[/tex]

[tex]M_2=\log(\dfrac{I_2}{I_0})\\\Rightarrow I_010^{M_2}=I_2\\\Rightarrow I_2=I_010^{5.1}[/tex]

Dividing the above intensities with each other we get

[tex]\dfrac{I_1}{I_2}=\dfrac{I_010^{6.7}}{I_010^{5.1}}\\\Rightarrow \dfrac{I_1}{I_2}=39.81\approx 40\\\Rightarrow I_1=40I_2[/tex]

The intensity of the earthquake in 1994 was 40 times stronger than the earthquake in 2014.

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