Video Captions: Algebra Applications: How Is Earthquake Magnitude Measured?

An earthquake is a vibration in the Earth's crust.

All vibrations are waves that can be modeled by a trigonometric

function, like the one shown here.

The height of the wave above the x-axis is called

the amplitude.

When an earthquake occurs a seismic wave is produced.

An instrument called a seismograph is used to detect

the seismic wave.

The measure of the amplitude is used in this formula to

find the magnitude of the earthquake.

Notice that this is a logarithmic function.

Once the magnitude is measured, using the

exponential function ten to the X gives the intensity of

the earthquake.

To see how dramatic the changes are in the amplitude

of a seismic wave we can link the coordinates of the

exponential function to the amplitude.

Turn on 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.

Place a point on the graph of the exponential function, then

press ESCAPE.

Move the pointer to the Y coordinate of the point.

Recall that this is the value of the earthquake intensity.

Press the variable key then one.

You will be storing the value of this coordinate in the

variable A.

Now graph the sine curve, but link the value of the

amplitude to the variable A.

We now need to change the window settings.

The x-axis should go from zero to ten to approximate the

range of values for the magnitude.

The y-axis, on the other hand, should extend to at least

one billion.

So, press MENU, and under WINDOW ZOOM select

WINDOW SETTINGS.

Change xMin to negative one, press the TAB key, and change

xMax to ten.

Tab to yMin and change it to negative one billion.

Press the TAB key and change yMax to positive one billion,

then tab your way to OK and press ENTER.

Now use the nav pad to hover over the point on the

exponential graph.

Click and hold to grasp the point.

Use the RIGHT ARROW to move the point to higher

values of X.

Although the sine curve is there you can't see it until

the value of X in the exponential function is

greater than five.

This corresponds to a low rumbling but not very

powerful earthquake.

But as X approaches ten the sine curve explodes into view.

This shows just how rapidly the earthquake becomes

powerful and extremely damaging.

For example, move the point from an X coordinate of five

to an X coordinate of nine.

The sine curve grows dramatically in size and shows

that a magnitude eight earthquake is ten thousand

times more powerful than one of magnitude five.

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