Richterville Earthquake

Algebra Level pending

The Richter Scale formula is used for calculating the intensities of earthquakes relative to each other, given here $M = log_{10}(\frac{I}{I_{0}})$ , where $M$ is the magnitude on the Richter Scale $I$ is the intensity of the earthquake being measured and $I_{0}$ is the intensity of a given reference earthquake.

How many more times more intense is the 1985 Mexico City earthquake compared to the 2018 Richterville Earthquake Where the intensity of the 1985 Mexico City quake was $10^{8.0}$ and the 2018 Richterville quake was $10^{7.2}$

Round your answer to the nearest tenth

The answer is 6.3.

1 solution

Dylan Vermette
Apr 28, 2018

From the Richter Scale formula we can deduce that $10^M = \frac{I}{I_{0}}$

$\frac{I}{I_{0}}$ is exactly what we want because it is the ratio of the intensity of the measured earthquake to the reference earthquake

We know the intensity of the measured earthquake (that is the 1985 Mexico City quake) as being $10^{8.0}$ and the intensity of the 2018 Richterville earthquake being $10^{7.2}$ So then this ratio is $\frac{10^{8.0}}{10^{7.2}}$ or $10^{0.8}$ we evaluate this answer to be roughly $6.31$ rounding to the nearest tenth we get $\boxed{6.3}$

Richterville Earthquake

The answer is 6.3.

1 solution

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