document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188722>Question 1188722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A culture of bacteria triples every 8 hours. if there are 100 bacteria now, and 2700 bacteria after 24 hours, find the bacteria population 2 hours earlier </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819875 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the bacteria triples every 8 hours.<BR>\n" );
document.write( "there are 100 now.<BR>\n" );
document.write( "there are 300 in 8 hours.<BR>\n" );
document.write( "there are 900 in 16 hours.<BR>\n" );
document.write( "there are 2700 in 24 hours.\r<BR>\n" );
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document.write( "the growth is exponential.\r<BR>\n" );
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document.write( "let x = the rate of growth each hour.\r<BR>\n" );
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document.write( "you get 300 = 100 * x^8\r<BR>\n" );
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document.write( "divide both sides by 100 to get:\r<BR>\n" );
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document.write( "3 = x^8\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 3 ^ (1/8) = 1.14720269.\r<BR>\n" );
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document.write( "that's the rate of growth every hour.\r<BR>\n" );
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document.write( "in 8 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 8 = 300.\r<BR>\n" );
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document.write( "in 16 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 16 = 900.\r<BR>\n" );
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document.write( "in 24 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 24 = 2700.\r<BR>\n" );
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document.write( "in 22 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 22 = 2051.556351.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "the equation can be graphed as shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/121101.jpg\" >\r<BR>\n" );
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document.write( "coordinate points are in (x,y) format.<BR>\n" );
document.write( "x is the number of hours.<BR>\n" );
document.write( "y is the number of bacteria.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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