4.5 - Exponential and Logarithmic Models

4.5 - Exponential and Logarithmic Models - <?xml...

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<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>4.5 - Exponential and Logarithmic Models</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> <style type="text/css"> <!-- h3 { clear: none; } --> </style> </head> <body> <h1>4.5 - Exponential and Logarithmic Models</h1> <h2>Exponential Growth</h2> <h3><img src="growth.gif" alt="Exponential growth model" width="315" height="285" class="imgrt" />Function</h3> <p>y = C e<sup>kt</sup>, k > 0</p> <h3>Features</h3> <ul> <li> Asymptotic to y = 0 to left</li> <li>Passes through (0,C)</li> <li>C is the initial value</li> <li> Increases without bound to right</li> </ul> <h3>Notes</h3> <p>Some of the things that exponential growth is used to model include population growth, bacterial growth, and compound interest. </p> <p>If you are lucky enough to be given the initial value, that is the value when x = 0, then you already know the value of the constant C. The only thing necessary to complete the model is to have one additional point on the graph. Plug in the values for x, y, and C, and solve for k. </p> <p>Alternatively, almost like cheating, you can put the x-values into List 1, the y-values into List 2, and choose the ExpReg option on the TI-82 calculator.</p> <h2>Exponential Decay (decreasing form)</h2> <h3><img src="decay.gif" alt="Exponential decay model" width="315" height="285" class="imgrt" />Function</h3> <p>y = C e<sup>-kt</sup>, k > 0</p> <h3>Features</h3> <ul> <li>Asymptotic to y = 0 to right</li> <li> Passes through (0,C)</li> <li> C is the initial value</li> <li> Decreasing, but bounded below by y=0</li> </ul> <h3>Notes</h3> <p>Exponential decay and be used to model radioactive decay and depreciation. </p>
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4.5 - Exponential and Logarithmic Models - &lt;?xml...

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