Video Captions: Algebra Applications: Exponential Functions

[Music]

Narrator: In August 2008, China hosted the Olympics to

great fanfare.

But only a few months earlier China was host to an unwelcome

guest, a massive earthquake that devastated the

Sichuan Province.

As a result of the earthquake of May 8, 2008 nearly seventy

thousand people died and millions were left homeless.

The magnitude of the earthquake at its epicenter

was seven point nine on the Richter scale.

As the name suggests, the epicenter is where the most

damage occurs.

As you get farther away from the epicenter there is

less damage.

In fact, the amount of damage decreases dramatically.

This suggests that the magnitude of an earthquake

changes in a non-linear fashion.

This color-coded map from the US Geological Survey shows the

intensity of the earthquake near the epicenter.

The red areas are where the most intense earthquake

activity occurred.

The green area showed moderate activity.

The distance from the red area to the green area is about one

hundred and fifty kilometers, or about one hundred miles, a

very short distance compared to the overall size of

the earthquake.

Because of the dramatic changes in intensity from one

point to another earthquakes are an ideal example of

exponential functions.

Unlike a linear function, which changes in value in a

constant way, exponential functions change value in

big leaps.

If earthquake intensity could be modeled using a linear

function then the map would show a gradual change from red

to green, so that a larger area would be affected by

the earthquake.

Instead a non-linear function, in this case an exponential

function, shows the worst of the earthquake damage

localized to a relatively small area.

Exponential functions and their inverses provide ideal

models for us to better understand earthquakes, but

before applying these mathematical models let's

first get a better understanding of what an earthquake is.