document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159189>Question 1159189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The count in a bacteria culture was 600 after 10 minutes and 2000 after 35 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 120 minutes. <BR>\n" );
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document.write( "When will the population reach 10000 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782276 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=782276\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The count in a bacteria culture was 600 after 10 minutes and 2000 after 35 minutes.<BR>\n" );
document.write( " Assuming the count grows exponentially,<BR>\n" );
document.write( "Using the form that a*b^x = y<BR>\n" );
document.write( "x=10, y=600<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ab%5E10+=+600 ALIGN=MIDDLE  ALT=\"a%2Ab%5E10+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+600%2Fb%5E10 ALIGN=MIDDLE  ALT=\"a+=+600%2Fb%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=35, y=2000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ab%5E35+=+2000 ALIGN=MIDDLE  ALT=\"a%2Ab%5E35+=+2000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "replace a with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2Fb%5E10 ALIGN=MIDDLE  ALT=\"600%2Fb%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28600%2Fb%5E10%29%2Ab%5E35+=+2000 ALIGN=MIDDLE  ALT=\"%28600%2Fb%5E10%29%2Ab%5E35+=+2000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancel b^10<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2Ab%5E25+=+2000 ALIGN=MIDDLE  ALT=\"600%2Ab%5E25+=+2000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E25+=+2000%2F600 ALIGN=MIDDLE  ALT=\"b%5E25+=+2000%2F600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E25+=+20%2F6 ALIGN=MIDDLE  ALT=\"b%5E25+=+20%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Aln%28b%29+=+ln%283.333%29 ALIGN=MIDDLE  ALT=\"25%2Aln%28b%29+=+ln%283.333%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ln(b) = ln(3.333)/25}}}<BR>\n" );
document.write( "ln(b) = .048159<BR>\n" );
document.write( "b = 1.049337<BR>\n" );
document.write( "Find a<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2F1.048337%5E10 ALIGN=MIDDLE  ALT=\"600%2F1.048337%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2F1.6186 ALIGN=MIDDLE  ALT=\"600%2F1.6186\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 370.7<BR>\n" );
document.write( "The equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+370.7%2A1.049337%5Ex%29 ALIGN=MIDDLE  ALT=\"y+=+370.7%2A1.049337%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "What was the initial size of the culture?<BR>\n" );
document.write( "x=0, therefore 370.7 is the initial amt<BR>\n" );
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document.write( "Find the doubling period.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.049337%5Ex+=+2 ALIGN=MIDDLE  ALT=\"1.049337%5Ex+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x*ln(1.049337) = ln(2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+ln%282%29%2Fln%281.049337%29 ALIGN=MIDDLE  ALT=\"x+=+ln%282%29%2Fln%281.049337%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 14.4 min<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the population after 120 minutes.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+370.7%2A1.049337%5E120%29 ALIGN=MIDDLE  ALT=\"y+=+370.7%2A1.049337%5E120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 370.7*323.443<BR>\n" );
document.write( "y = 119,900.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "When will the population reach 10000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=370.7%2A1.049337%5Ex+=+10000 ALIGN=MIDDLE  ALT=\"370.7%2A1.049337%5Ex+=+10000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.049337%5Ex+=+10000%2F370.7 ALIGN=MIDDLE  ALT=\"1.049337%5Ex+=+10000%2F370.7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.049337%5Ex+=+26.976 ALIGN=MIDDLE  ALT=\"1.049337%5Ex+=+26.976\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x*ln(1.049337) = ln(26.976)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+ln%2826.976%29%2Fln%281.049337%29 ALIGN=MIDDLE  ALT=\"x+=+ln%2826.976%29%2Fln%281.049337%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 68.42 min<BR>\n" );
document.write( ":<BR>\n" );
document.write( "looks like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-50%2C+150%2C+-20000%2C+100000%2C+370.7%2A1.049337%5Ex%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-50%2C+150%2C+-20000%2C+100000%2C+370.7%2A1.049337%5Ex%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );