# Exponential and Logarithmic Models

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http://earthquake.usgs.gov/.

"The earthquake with a magnitude 8 releases a million times more energy than an earthquake with magnitude 4."

Assess the accuracy of this statement. Explain your answer in mathematical terms.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

The energy in an earthquake is approximately proportional to 10^(3M/2) where M is the magnitude.

For M = 8, E is approximately proportional to 10^(3x8/2) = 10^12

For M = 4, E is approximately proportional to 10^(3x4/2) = 10^6

Dividing (M = 8) / (M = 40 gives an energy ratio of (10^12) / (10^6) = 10^6 which is a million times more for M =8 compared to M =4.

Â© BrainMass Inc. brainmass.com September 27, 2022, 5:00 pm ad1c9bdddf>https://brainmass.com/math/number-theory/exponential-and-logarithmic-models-587256