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<p>[QUOTE="-jeffB, post: 2260686, member: 27832"]You know what generates an exponential curve?</p><p><br /></p><p>Any exponential function.</p><p><br /></p><p>What's a good example of an exponential function?</p><p><br /></p><p>Any annual <i>percentage</i> increase.</p><p><br /></p><p>20% inflation? EXPONENTIAL GROWTH!</p><p><br /></p><p>0.2% inflation? EXPONENTIAL GROWTH!</p><p><br /></p><p>1% annual salary increase? EXPONENTIAL GROWTH!</p><p><br /></p><p>Even funnier is when PM enthusiasts breathlessly observe that metal prices are about to "go parabolic". "Parabolic" growth is <i>slower</i>, over the long term, than exponential growth. If <b>X</b> counts the years, "parabolic" growth (<b>X^2</b>, or <b>X^n</b> for <i>any</i> value of <b>n</b>, however large) will eventually be overtaken and dwarfed by simple compound interest (<b>(1 + r)^X</b>, for <i>any</i> positive value of <b>r</b>, however small).</p><p><br /></p><p>But misuse of mathematical terms is usually the least of the problems in those sorts of discussions...[/QUOTE]</p><p><br /></p>
[QUOTE="-jeffB, post: 2260686, member: 27832"]You know what generates an exponential curve? Any exponential function. What's a good example of an exponential function? Any annual [I]percentage[/I] increase. 20% inflation? EXPONENTIAL GROWTH! 0.2% inflation? EXPONENTIAL GROWTH! 1% annual salary increase? EXPONENTIAL GROWTH! Even funnier is when PM enthusiasts breathlessly observe that metal prices are about to "go parabolic". "Parabolic" growth is [I]slower[/I], over the long term, than exponential growth. If [B]X[/B] counts the years, "parabolic" growth ([B]X^2[/B], or [B]X^n[/B] for [I]any[/I] value of [B]n[/B], however large) will eventually be overtaken and dwarfed by simple compound interest ([B](1 + r)^X[/B], for [I]any[/I] positive value of [B]r[/B], however small). But misuse of mathematical terms is usually the least of the problems in those sorts of discussions...[/QUOTE]
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