document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198940>Question 1198940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The count in a bacteria culture was 600 after 20 minutes and 1600 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 60 minutes. <BR>\n" );
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document.write( "When will the population reach 13000. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832634 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "general exponential models <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%2Ab%5Et ALIGN=MIDDLE  ALT=\"y+=+a%2Ab%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the time from the starting moment and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is some arbitrary base\r<BR>\n" );
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document.write( "if the count in a bacteria culture was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600 ALIGN=MIDDLE  ALT=\"600\"   DISABLED_style= \"max-width:90%; height:auto;\" > after<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20 ALIGN=MIDDLE  ALT=\"+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes,we have \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600+=+a%2Ab%5E20 ALIGN=MIDDLE  ALT=\"600+=+a%2Ab%5E20\"   DISABLED_style= \"max-width:90%; height:auto;\" >............eq.1........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=600%2Fb%5E20+ ALIGN=MIDDLE  ALT=\"a=600%2Fb%5E20+\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.1a\r<BR>\n" );
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document.write( "if the count in a bacteria culture was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600 ALIGN=MIDDLE  ALT=\"1600\"   DISABLED_style= \"max-width:90%; height:auto;\" > after<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30 ALIGN=MIDDLE  ALT=\"+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes,we have \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600+=+a%2Ab%5E30 ALIGN=MIDDLE  ALT=\"1600+=+a%2Ab%5E30\"   DISABLED_style= \"max-width:90%; height:auto;\" >............eq.2, sustitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600+=+%28600%2Fb%5E20+%29%2Ab%5E30 ALIGN=MIDDLE  ALT=\"1600+=+%28600%2Fb%5E20+%29%2Ab%5E30\"   DISABLED_style= \"max-width:90%; height:auto;\" >............simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600+=+600%2Ab%5E10 ALIGN=MIDDLE  ALT=\"1600+=+600%2Ab%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600%2F600=b%5E10 ALIGN=MIDDLE  ALT=\"1600%2F600=b%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F3=b%5E10 ALIGN=MIDDLE  ALT=\"8%2F3=b%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=root%2810%2C8%2F3%29 ALIGN=MIDDLE  ALT=\"b=root%2810%2C8%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=600%2Fb%5E20+ ALIGN=MIDDLE  ALT=\"a=600%2Fb%5E20+\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.1a\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F3=b%5E10 ALIGN=MIDDLE  ALT=\"8%2F3=b%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F3%29%5E2=b%5E20 ALIGN=MIDDLE  ALT=\"%288%2F3%29%5E2=b%5E20\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E20=64%2F9 ALIGN=MIDDLE  ALT=\"b%5E20=64%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=600%2F%2864%2F9%29+ ALIGN=MIDDLE  ALT=\"a=600%2F%2864%2F9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=675%2F8 ALIGN=MIDDLE  ALT=\"a=675%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "general exponential models <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28675%2F8%29%2A%28root%2810%2C8%2F3%29%29%5Et ALIGN=MIDDLE  ALT=\"y+=+%28675%2F8%29%2A%28root%2810%2C8%2F3%29%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What was the initial size of the culture?\r<BR>\n" );
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document.write( "the initial population \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" was<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=675%2F8 ALIGN=MIDDLE  ALT=\"675%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The doubling period equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5Et+=+2 ALIGN=MIDDLE  ALT=\"+b%5Et+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%2810%2C8%2F3%29%5Et+=+2 ALIGN=MIDDLE  ALT=\"root%2810%2C8%2F3%29%5Et+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28root%2810%2C8%2F3%29%5Et%29+=+log%282%29 ALIGN=MIDDLE  ALT=\"log%28root%2810%2C8%2F3%29%5Et%29+=+log%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Alog%28root%2810%2C8%2F3%29%29+=+log%282%29 ALIGN=MIDDLE  ALT=\"t%2Alog%28root%2810%2C8%2F3%29%29+=+log%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+log%282%29%2Flog%28root%2810%2C8%2F3%29%29+ ALIGN=MIDDLE  ALT=\"t=+log%282%29%2Flog%28root%2810%2C8%2F3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+log%282%29%2Flog%28root%2810%2C8%2F3%29%29+ ALIGN=MIDDLE  ALT=\"t=+log%282%29%2Flog%28root%2810%2C8%2F3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=7.06695min ALIGN=MIDDLE  ALT=\"t=7.06695min\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the population after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28675%2F8%29%2A%28root%2810%2C8%2F3%29%29%5E60 ALIGN=MIDDLE  ALT=\"y+=+%28675%2F8%29%2A%28root%2810%2C8%2F3%29%29%5E60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+819200%2F27 ALIGN=MIDDLE  ALT=\"y+=+819200%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=30340.74 ALIGN=MIDDLE  ALT=\"y=30340.74\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When will the population reach <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13000 ALIGN=MIDDLE  ALT=\"13000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13000=+%28675%2F8%29%2A%28root%2810%2C8%2F3%29%29%5Et ALIGN=MIDDLE  ALT=\"13000=+%28675%2F8%29%2A%28root%2810%2C8%2F3%29%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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