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Determine how the energies of two earthquakes differing by 2.5 in their magnitude are related.

5623 times

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

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Determine how the energies…

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02:46

01:10

Determine the energy of an…

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04:48

Suppose that the magnitude…

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If one earthquake has a ma…

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Determine the magnitude of…

What is the relation between two earthquakes, energies with a 2.5 magnitude difference. We're going to be using this basic equation here relating magnitude and energy of earthquakes on the Richter scale. So let's start by identifying an equation here for each of these two earthquake. So the first of which will have log E. And let's call this E one. The energy for this first earthquake is equal to 11.8 Plus 1.5 M. It's just a basic equation. The second one here will be log E. Let's call this E two for the second earthquake is equal to 11.8 Plus 1.5 And plus 2.5. So for this one we have this magnitude plus 2.5 to account for that 2.5 magnitude difference that was given to us in the question. So we're going to subtract these equations from one another, which gives us law G2 minus log E one And that will be equal to 3.75 And 3.75 makes sense because if we take 11.8 -11.8, those will cancel 1.5 M minus the 1.5 M. That we would get by multiplying these out would also cancel. And then we're just left with 1.5 times 2.5, Which gives us this 3.75. Our next step is going to be to rewrite this, but in exponential or as a single algorithm, So that will give us log E two Divided by 81 Is equal to 3.75. Now we can rewrite this in exponential form. So we've got E two divided by E one is equal to 10 to the power of 3.75, 10 to the power of 3.75 is about equal to 5,623. Now, if we wanted to solve for E to hear what we'll see is that E two is equal to 5623 Times E one. So this is saying that the energy of E2, given its magnitude difference or that increased magnitude 2.5, It means it's going to have energy that's about 5,623 times greater than the energy of E one. So we can write that equation to give us that relationship. Or we could also say that it will, the energy will be 5623 times larger.

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