# Applications of Exponential Functions

## Word problems with variables as exponents

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Population Explosion

Scientists use functions to predict how quickly populations of plants and animals grow. If you can write a function to describe population growth, you can create a graph to show how many plants or animals will exist at a certain point in time. Certain organisms can reproduce very quickly. Under the right conditions, a single cell can create an explosion of new life.

In some parts of the world, the red tide is an annual event. During the red tide, the sea changes color as algae take over the surface. Scientists call these events harmful algal blooms (HAB). During a HAB, algae can double its population once, twice, or even three times a day. This population growth is an example of an exponential function. In a very short time, these microscopic organisms can completely cover the surface of the water.

Credit: Alejandro D?az
Source: http://commons.wikimedia.org/wiki/File:La-Jolla-Red-Tide.780.jpg
License: CC BY-NC 3.0

Some HABs release poisons into the water, which can kill fish and other marine life. Shellfish can absorb the poisons, making them toxic. Thus, when an area suffers from a HAB, local fisherman and restaurants suffer too. Scientists believe that the use of fertilizer has made HABs more common and more dangerous. After a farmer fertilizes his fields, rain washes the fertilizer into streams and rivers. This run-off can travel to the sea, where it feeds algal blooms, enabling the algae's explosive population growth.

See for yourself: http://www.youtube.com/watch?v=XTw712ODULU

#### Explore More

Find out how scientists track HABs and learn more about the effects of algal blooms by watching the following videos.

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