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Determine the energy of an earthquake if its magnitude is $3.8 .$

$$3.16 \times 10^{17} \text { ergs }$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:03

Determine the energy of an…

01:09

01:06

01:10

01:02

Determine the magnitude of…

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01:05

02:46

Determine how the energies…

01:31

The magnitude $M$ of an ea…

00:30

One earthquake has magnitu…

02:47

Recall the formula for cal…

02:06

EARTHQUAKES Anchorage, Ala…

If the magnitude of an earthquake is 3.8, what is its energy? So let's start by plugging in the information that we do have to this equation written in green. So we've got that the log of energy, which we don't have yet is equal to 11.8 plus 1.5 times are magnitude. Which is given to us to be 3.8. Let's simplify that right hand side which would leave us with the log of E is equal to 17.5. Now at this point we want to go ahead and rewrite this in exponential form Which gives us E. is equal to 10 to the power of 17.5. And we can just calculate that and then rewrite in scientific notation to give ourselves an energy of this earthquake which is equal to 3.16 times 10 to the 17th power. And this is a measurement of er eggs.

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