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Determine how the energies of two earthquakes differing by 1.5 in their magnitude are related.

178 times

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Oregon State University

McMaster University

Harvey Mudd College

Idaho State University

Lectures

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Determine how the energies…

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Suppose that the magnitude…

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Determine the energy of an…

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If one earthquake has a ma…

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Determine the magnitude of…

This question, we're looking at the relation between two earthquakes energy with a 1.5 difference in their magnitude. So we're still going to be using this equation that relates magnitude and energy on the Richter scale. But we need to rewrite this equation for these two different earthquakes that have this 1.5 magnitude difference. So let's start with one earthquake. So this first one is just going to have this typical equation, log E is equal to 11.8 plus 1.5 M. Whatever its energy or whatever its magnitude happens to be. The 2nd 1, however, is going to have Log E is equal to 11.8 Plus 1.5 And plus 1.5 because that's going to account for that difference in our magnitudes. Now we can see between the blue equation and the yellow equation, we have that difference in magnitude of 1.5 recognized. So let's start by subtracting these from one another. So actually let's go ahead and call this first one log E one and let's call the second one, log E two because there are different energies. So let's now subtract them from one another. So we'll take law G2 -61. If we subtract these from one another we get 2.25 And you can see that are 11.8 would have cancelled out, our 1.5 M. S would cancel out. And we would be just left with 1.5 times 1.5 which gives us this 2.5 right here. Now that we have this, we can rewrite this into a single law algorithm. So we end up with log E two Divided by E one Is equal to 2.25. Let's go ahead and rewrite this in exponential form, which gives us E two divided by E one is equal to 10 to the power of 2.25, 10 to the power of 2.25 is about equal to 177.8- seven. So therefore what we're seeing here. If we were to solve for E2, You see, we have E2 is about equal to let's round that to 178 Times E one. So this is telling us that this magnitude difference of 1.5 translates into this. Energy being increased by a factor of about 178, Meaning that the energy between these two earthquakes, the one with that magnitude that's 1.5 points greater in magnitude has about 178 times the energy as the other one.

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