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Determine the energy of an earthquake if its magnitude is $8.5 .$

$$3.55 \times 10^{24} \text { ergs }$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Missouri State University

McMaster University

Harvey Mudd College

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Determine the energy of an…

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Determine the magnitude of…

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EARTHQUAKES Anchorage, Ala…

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The magnitude $M$ of an ea…

Anchorage, Alaska, had a m…

If an earthquake has a magnitude of 8.5, what is its energy? And to find that we'll be using this function here, which gives us that relationship between magnitude and energy of an earthquake on the Richter scale. Let's start by plugging in the information we do have. So left hand side is going to stay as log E, which is equal to 11.8 Plus 1.5. And now it's plug in 8.5. The magnitude that was given to us Simplify that right hand side which will leave us with log of E is equal to 24.55. Rewriting this now in exponential form. Well give us E is equal to 10 to the power of 24.55, calculating that. And then rewriting in scientific notation, which your calculators should actually give you its answer and will tell us that the energy is equal to 3.5 times 10 to the power of 24 in the measurement of er eggs.

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