document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190197>Question 190197</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495013579/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Trying to figure out the Discovery Project on Exponential Explosion.\r<BR>\n" );
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document.write( "It doesn't really give any formula other than f(x)=2^x.\r<BR>\n" );
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document.write( "So I used this formula for the answers.\r<BR>\n" );
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document.write( "But when I read back into the section it shows another formula for the growth of viruses. So I am not sure which to use. \r<BR>\n" );
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document.write( "Thanks!  </SPAN>\n" );
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document.write( "I can't tell what your \"Discovery Project on Exponential Explosion\" looks like, so I'm guessing somewhat.  But here is what I know.\r<BR>\n" );
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document.write( "The general formula for exponential growth of an organism is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ N_t = N_oP^t\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE N_o\"> is the initial number of organisms, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P\"> is the number of progeny per generation, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\"> is the number of generations, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE N_t\"> is the number of organisms after <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\"> generations.\r<BR>\n" );
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document.write( "The formula you gave, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x) = 2^x\"> is a reduction of the general formula above where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE N_t = f(x)\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE N_o = 1\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P = 2\"> (or 2 progeny per generation), and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> is the number of generations.\r<BR>\n" );
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document.write( "These numbers actually model the exponential growth of bacteria, because you get 2 cells, i.e. 2 progeny, each time a cell splits.  Viruses, on the other hand, produce 100s and even 1000s of progeny each generation.  The various Rhinoviruses (major cause of the common cold) can replicate 100000 progeny per generation.\r<BR>\n" );
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document.write( "What I think is going on is that your particular Discovery Project is asking you to look first at the exponential growth of <i><b>bacteria</b></i> as a beginning baseline for your understanding of exponetial growth.  If not, and they are really talking about viruses, the only thing left to do is get clarification from your instructor.\r<BR>\n" );
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document.write( "Hope that helps.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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