document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005594>Question 1005594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bacteria were introduced to a petri dish. Two hours after the introduction, there were 120411 bacteria. After seven hours since the introduction, there were 1083699 bacteria.\r<BR>\n" );
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document.write( "1.) Find the growth rate of the bacteria. (round to 3 decimal places)\r<BR>\n" );
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document.write( "2.) How many bacteria were initially introduced to the Petri dish? (Round to the nearest bacteria).\r<BR>\n" );
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document.write( "3.) How many bacteria will there be after 12 hours? (Round to the nearest bacteria).\r<BR>\n" );
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document.write( "4.) How long does it take for the bacteria colony to reach 361233 bacteria? (round to 2 decimal places)\r<BR>\n" );
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document.write( "Use Pe^rt equation!\r<BR>\n" );
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document.write( "PLEASE HELP ME ! I really have to understand this ! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621811 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = amount of bacteria after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+P%2Ae%5E%28r%2At%29+ ALIGN=MIDDLE  ALT=\"+A+=+P%2Ae%5E%28r%2At%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You are given 2 points on this growth curve:<BR>\n" );
document.write( "( 2, 120411 ) and ( 7, 1083699 )<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "That will give you 2 equations with 2 unknowns,<BR>\n" );
document.write( "so it is solvable<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120411+=+P%2Ae%5E%28r%2A2%29+ ALIGN=MIDDLE  ALT=\"+120411+=+P%2Ae%5E%28r%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1083699+=+P%2Ae%5E%28r%2A7%29+ ALIGN=MIDDLE  ALT=\"+1083699+=+P%2Ae%5E%28r%2A7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(1)<BR>\n" );
document.write( "You can solve both equations for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+120411+%2F+e%5E%28r%2A2%29+ ALIGN=MIDDLE  ALT=\"+P+=+120411+%2F+e%5E%28r%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+1083699+%2F+e%5E%28r%2A7%29+ ALIGN=MIDDLE  ALT=\"+P+=+1083699+%2F+e%5E%28r%2A7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Substitute (a) into (b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120411+%2F+e%5E%28r%2A2%29+=+1083699+%2F++e%5E%28r%2A7%29+ ALIGN=MIDDLE  ALT=\"+120411+%2F+e%5E%28r%2A2%29+=+1083699+%2F++e%5E%28r%2A7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28r%2A7%29+ ALIGN=MIDDLE  ALT=\"+e%5E%28r%2A7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++1083699+=+120411+%2A%28+e%5E%28r%2A7%29+%2F+e%5E%28r%2A2%29%29+ ALIGN=MIDDLE  ALT=\"++1083699+=+120411+%2A%28+e%5E%28r%2A7%29+%2F+e%5E%28r%2A2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120411+ ALIGN=MIDDLE  ALT=\"+120411+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28r%2A7%29+%2F+e%5E%28r%2A2%29+=+1083699+%2F+120411+ ALIGN=MIDDLE  ALT=\"+e%5E%28r%2A7%29+%2F+e%5E%28r%2A2%29+=+1083699+%2F+120411+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28r%2A5%29+=+9+ ALIGN=MIDDLE  ALT=\"+e%5E%28r%2A5%29+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Take the natural log of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+e%5E%28r%2A5%29%29+=+ln%289%29+ ALIGN=MIDDLE  ALT=\"+ln%28+e%5E%28r%2A5%29%29+=+ln%289%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%2A5+=+2.1972+ ALIGN=MIDDLE  ALT=\"+r%2A5+=+2.1972+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+.439+ ALIGN=MIDDLE  ALT=\"+r+=+.439+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "Plug this result back into either (a) or (b)<BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120411+=+P%2Ae%5E%28r%2A2%29+ ALIGN=MIDDLE  ALT=\"+120411+=+P%2Ae%5E%28r%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120411+=+P%2Ae%5E%28.439%2A2%29+ ALIGN=MIDDLE  ALT=\"+120411+=+P%2Ae%5E%28.439%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120411+=+P%2Ae%5E.879+ ALIGN=MIDDLE  ALT=\"+120411+=+P%2Ae%5E.879+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120411+=+P%2A2.408+ ALIGN=MIDDLE  ALT=\"+120411+=+P%2A2.408+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+50005+ ALIGN=MIDDLE  ALT=\"+P+=+50005+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+12+ ALIGN=MIDDLE  ALT=\"+t+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+P%2Ae%5E%28r%2At%29+ ALIGN=MIDDLE  ALT=\"+A+=+P%2Ae%5E%28r%2At%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+=+50005%2Ae%5E%28.439%2A12+%29+ ALIGN=MIDDLE  ALT=\"+A+=+50005%2Ae%5E%28.439%2A12+%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+=+50005%2Ae%5E5.268+ ALIGN=MIDDLE  ALT=\"+A+=+50005%2Ae%5E5.268+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+50005%2A194.03+ ALIGN=MIDDLE  ALT=\"+A+=+50005%2A194.03+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+9702346+ ALIGN=MIDDLE  ALT=\"+A+=+9702346+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "(4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+P%2Ae%5E%28r%2At%29+ ALIGN=MIDDLE  ALT=\"+A+=+P%2Ae%5E%28r%2At%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+361233+=+50005%2Ae%5E%28.439t%29+ ALIGN=MIDDLE  ALT=\"+361233+=+50005%2Ae%5E%28.439t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28.439t%29+=+361233%2F50005+ ALIGN=MIDDLE  ALT=\"+e%5E%28.439t%29+=+361233%2F50005+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28.439t%29+=+7.22394++ ALIGN=MIDDLE  ALT=\"+e%5E%28.439t%29+=+7.22394++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+e%5E%28.439t%29%29+=+ln%287.22394+%29+ ALIGN=MIDDLE  ALT=\"+ln%28+e%5E%28.439t%29%29+=+ln%287.22394+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.439t+=+1.9774+ ALIGN=MIDDLE  ALT=\"+.439t+=+1.9774+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+4.50+ ALIGN=MIDDLE  ALT=\"+t+=+4.50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "I could easily have made some mistakes, but<BR>\n" );
document.write( "I'm pretty sure my methods are OK<BR>\n" );
document.write( "You could get other opinions, too.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );