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Unformatted text preview: Math Learning Center Boise State ©2010 Modeling with non-linear functions STEM 8 Radicals appear in many situations in science including: Laws of Motion, Hookes Law, pendulum oscillation, Series RLC circuits (electronics), Maxwell-Boltzman distribution, and kinetic energy equations. Consider an object at rest. If we propel the object with a constant acceleration of uU¡¡g¢G £ and measure the time it takes to move in intervals of four meters, the collection of the first nine data points would create a graph that looks like Looking closely at that graph we find that initially there is a large increase in time as we increase the distance. However, as distance increases, a change in distance has less of an effect on the time. If we draw a curve through the points, we obtain the following: Looking at this graph, we should be able to recognize it as being similar to a square root graph. In fact, when we mathematically compare time ¤¥¦ to both distance traveled ¤§¦ and acceleration ¨ © uU¡¡g¢G £ , we find that the points observed follow the equation: 5 10 15 10 20 30 40 Time Distance 5 10 15 10 20 30 40 Time Distance Math Learning Center Boise State ©2010 g G ¡ ¢£ ¤ G ¡ ¢£ ¥u¦¦ Consider the Maxwell-Boltzman distribution in chemistry. One part of this relationship gives the average velocity, § ¨©ª , of gas molecules as the following relationship: § ¤«¬ G U®¯ °± ² ³ ¢ where § ¨©ª ´µ g¶· ¸¹·º¸»· ¹·¼½¾´g¿ ½À g¶· Á½¼·¾§¼·µ ® ´µ g¶· §Â´¹·ºµ¸¼ »¸µ ¾½Âµg¸Âg ·Ã§¸¼ g½ UuÄÅÆÇ È ÉÊË Ì ¯ ´µ g¶· g·ÁÍ·º¸g§º· ´Â Î·¼¹´ÂµÏ Ì ± ´µ g¶· Á½¼¸º Á¸µµ ´Â Ð ÉÊË Letting ® G UuÄÅÆÇ Ñ ÒÓÔ Õ and ± G ÖÇ ª ÒÓÔ our equation now will relate average velocity, § ¨©ª Ï to temperature, ¯u § ¤«¬ G U × UuÄÅÆÇ × ¯...
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