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Intermediate Value Theorem, Existence of Solutions

Continuity on an interval proves existence of values and heights within the interval.

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Credit: Ben Townsend
Source: http://en.wikipedia.org/wiki/File:Velociraptor_Wyoming_Dinosaur_Center.jpg
License: CC BY-NC 3.0

The atmosphere?s concentration of carbon dioxide (CO2) has been rising precipitously over the last 50 years. On the other hand, we know that in the past the CO2 levels have been both higher and lower than they are today. Because the graph of CO2 over time is continuous, scientists can find other time periods when CO2 levels were equal to the levels we have today. This lets them make predictions about how changes in CO2 levels will affect our climate and the world?s habitats.

Too Much of a Good Thing

CO2 is a greenhouse gas. It traps heat in the Earth?s atmosphere. Usually, this is a good thing. If we didn?t have greenhouse gasses, heat would move from the Earth out into space. Our planet would be a frozen wasteland, dead and lifeless. However, too much CO2 in the atmosphere could cause the Earth to grow warmer. For instance, in the past, carbon dioxide levels and global temperatures have been higher. While certain plants, animals, and insects thrived when temperatures were higher, human beings would have trouble living and growing food in a warmer world.

Currently, much of the research on carbon dioxide looks at how fossil fuels contribute to climate change. Most of the CO2 in the atmosphere comes from plants and animals. However, the fossil fuels that we burn marginally impact global CO2 concentrations. Ecologists fear that these little changes could have big impacts on the climate.

Credit: NASA Goddard
Source: http://www.flickr.com/photos/24662369@N07/7163119469
License: CC BY-NC 3.0

Changing CO2 levels could impact rainfall, weather, and the habitats of various plants and animals. However, cutting back on carbon emissions needs to be a global effort. While cleaner fuel sources and increased efficiency have let the United States dramatically reduce emissions, the carbon emissions of many other countries continue to grow. Scientists have suggested that these emissions may contribute to odd weather patterns, sea levels, and even obesity.

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Image Attributions

  1. [1]^ Credit: Ben Townsend; Source: http://en.wikipedia.org/wiki/File:Velociraptor_Wyoming_Dinosaur_Center.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: NASA Goddard; Source: http://www.flickr.com/photos/24662369@N07/7163119469; License: CC BY-NC 3.0

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