1.02.4.Literacy - 0.0000831529 Growth Authors: Bill Davis,...

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Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl ©1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 1.02 Natural Logs and Exponentials LITERACY · L.1) Write down e to four accurate decimals. Write down p to four accurate decimals. Has anyone ever succeeded in finding a pattern for all the decimals of either number? · L.2) Use the axes below to give hand sketches of the plots of f @ x D = e x and g @ x D = e - x Label each curve. Each of the plotted points is on at least one of the plots. - 1.0 - 0.5 0.0 0.5 1.0 1.5 2.0 x 1 2 3 4 5 6 7 · L.3) Are there numbers x that make e x negative? Are there numbers x that make e - x negative? · L.4) Use the axes below to give hand sketches of the plots of f @ x D = Log @ e x D and g @ x D = Log @ e - x D . Label each curve. Each of the plotted points is on at least one of the plots. - 2 - 1 1 2 x - 3 - 2 - 1 1 2 3 · L.5) Why do lots of folks say that exponential growth is awesome? Give a real-world situation that is modeled by exponential growth. · L.6) What is exponential decay? Give a real-world situation that is modeled by exponential decay. · L.7) What does a constant inflation rate have to do with exponential growth? What is it about exponential growth that makes high inflation rates scary? · L.8) When an underwater light beam is turned on in sea water, the resulting intensity of the light decays exponentially along the direction of the beam. In fact, in clear sea water, the approximate percentage of the original intensity x meters from the source measured along the beam is given by intensity @ x D = 100 e - 1.4 x Here is a calculation of intensity @ 10 D : Clear @ intensity, x D ; intensity @ x _ D = 100 E - 1.4 x ; intensity @ 10 D 0.0000831529 Use this calculation to help explain why in any ocean almost no plants can grow at a depth
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This note was uploaded on 10/11/2011 for the course MATH 241 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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1.02.4.Literacy - 0.0000831529 Growth Authors: Bill Davis,...

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