document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169252>Question 1169252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The count in a bateria culture was 400 after 10 minutes and 1200 after 30 minutes. Assuming the count grows exponentially,\r<BR>\n" );
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document.write( "What was the initial size of the culture? <BR>\n" );
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document.write( "Find the doubling period. <BR>\n" );
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document.write( "Find the population after 80 minutes. <BR>\n" );
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document.write( "When will the population reach 14000. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793900 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A=Aob^x<BR>\n" );
document.write( "400=Ao^b^10<BR>\n" );
document.write( "1200=Ao^b^30<BR>\n" );
document.write( "3=b^20<BR>\n" );
document.write( "b=3^(1/20)=1.056<BR>\n" );
document.write( "not rounding<BR>\n" );
document.write( "1200=Aob^30=Ao*3^1.5<BR>\n" );
document.write( "Ao=230.94 or 231 organisms<BR>\n" );
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document.write( "A=231*3^0.05^x<BR>\n" );
document.write( "Doubling is when<BR>\n" );
document.write( "2=3^0.05^x<BR>\n" );
document.write( "or ln 2=x ln 3^0.05<BR>\n" );
document.write( "ln2=0.05x ln 3<BR>\n" );
document.write( "20 ln2=x ln3<BR>\n" );
document.write( "x=12.619 min or 12.6 min.<BR>\n" );
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document.write( "tripling time is 3=1.056^x or <BR>\n" );
document.write( "20 ln 3=x ln 3<BR>\n" );
document.write( "x=20 minutes, which it should be.<BR>\n" );
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document.write( "after 80 minutes<BR>\n" );
document.write( "A=231(3^0.05)^80=231^3^4<BR>\n" );
document.write( "=18,711 organisms<BR>\n" );
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document.write( "14000=231*3^0.05x<BR>\n" );
document.write( "60.606=3^(0.05)^x <BR>\n" );
document.write( "ln 60.606=x*0.05 ln 3<BR>\n" );
document.write( "82.088=x ln3<BR>\n" );
document.write( "x=74.72 min\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C40%2C-100%2C2000%2C231%2A3%5E%280.05x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C40%2C-100%2C2000%2C231%2A3%5E%280.05x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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