Video Captions: Algebra Applications: What Is the Difference Between Earthquake Intensity and Magnitude?

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The magnitude of an earthquake indicates how much damage

it caused.

So an earthquake of magnitude seven point nine causes much

more damage than one of magnitude five point zero.

But how much more?

The magnitude of an earthquake is related to its intensity

according to this exponential function.

Let's use this equation to compare two earthquakes that

occurred in the Sichuan Province.

In March 2009, a magnitude five point zero earthquake

struck the same region.

The ratio of the 2008 and 2009 earthquakes is shown.

The law of exponents allows us to express the ratio of the

powers of ten as shown.

Simplifying shows that the intensity of the 2008

earthquake is nearly eight hundred times larger than the

2009 earthquake.

So even though the magnitudes differ by three the

intensities differ by a significantly larger amount.

So when you hear something described as growing

exponentially now you can see how dramatic this

growth can be.

Magnitude, on the other hand, does not grow exponentially.

We can see this using the TI-Nspire.

Create a new document.

You may want to save your previous work, otherwise press

the TAB key and press ENTER.

Graph the function Y equals ten to the X.

This is the general form of the intensity equation

for an earthquake.

Now add three points to the graph.

Select the point on feature, then use the nav pad to add

three points to the graph.

We want to reflect the graph and the points across the line

of Y equals X.

To do so activate the line tool.

Use the nav pad to move the pointer to the origin.

Click once.

Then move the pointer to coordinate one comma one,

knowing that for now this is an estimate.

To adjust the line so that it is the graph of Y equals X

display the equation.

Press MENU and under ACTIONS select COORDINATES AND

EQUATIONS and then click twice on the graph.

You will see the equation of the line, which will likely

not be Y equals X.

To change the equation press ESCAPE, then move the pointer

to the line.

Press and hold the CLICK key then adjust the line up or

down until you see Y equals X.

We are now ready to reflect the exponential graph across

the line Y equals X.

Why do this?

The reflected graph is the inverse of the exponential.

Press MENU and under TRANSFORMATION

select REFLECTION.

Use the nav pad to click on one of the points on the

exponential graph.

Then click on the graph of Y equals X.

You'll see the reflective point below the graph of

Y equals X.

Repeat with the other two points.

Try to get your screen to look like this.

You can see the graph of the inverse taking shape.

To see the entire graph that fits the three points use the

locus of points tool.

Click on MENU, and under CONSTRUCTION select LOCUS.

Use the nav pad to move the pointer above one of the

points on the exponential graph.

Click to select it.

Then use the nav pad to select the corresponding

reflected point.

When you do you will see the inverse graph.

Try to get your screen to look like this.

You can now see that the graph of the inverse is a mirror

image of the exponential graph, if you consider the

line Y equals X as the mirror.

Furthermore, if you display the three coordinates on the

inverse you'll see that they are mirror images of the

coordinates of the exponential function.

In fact, the inverse of ten to the X is log base 10 of X,

usually just written as log X.

As with all inverses, F inverse of F of X is

equal to X.

In other words the log of ten to the X is X.

What this means is that the exponential graph gives you

the intensity of the earthquake while the

logarithmic graph gives you the magnitude.

The exponential graph increases rapidly the way that

earthquake intensity does, while the logarithmic graph

increases slowly the way that earthquake magnitude does.

Now that you've seen the difference between intensity

and magnitude, here is something else to consider.

When an earthquake occurs what is felt is the intensity, but

what is measured is the magnitude, and so this brings

up the question: How is magnitude measured?