document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005660>Question 1005660</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. <BR>\n" );
document.write( "1.) Find the growth rate of the bacteria. (round to 3 decimal places) <BR>\n" );
document.write( "2.) How many bacteria were initially introduced to the Petri dish? (Round to the nearest bacteria). <BR>\n" );
document.write( "3.) How many bacteria will there be after 12 hours? (Round to the nearest bacteria). <BR>\n" );
document.write( "4.) How long does it take for the bacteria colony to reach 361233 bacteria? (round to 2 decimal places) <BR>\n" );
document.write( "Use Pe^rt equation! <BR>\n" );
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 #622125 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=622125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Bacteria were introduced to a petri dish.<BR>\n" );
document.write( " Two hours after the introduction, there were 120411 bacteria.<BR>\n" );
document.write( " After seven hours since the introduction, there were 1083699 bacteria.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1.) Find the growth rate of the bacteria. (round to 3 decimal places)<BR>\n" );
document.write( "Write an equation for each scenario<BR>\n" );
document.write( "P*e^(2r) = 120411<BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120411%2F%28e%5E%282r%29%29 ALIGN=MIDDLE  ALT=\"120411%2F%28e%5E%282r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "P*e^(7r) = 1083699<BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1083699%2F%28e%5E%287r%29%29 ALIGN=MIDDLE  ALT=\"1083699%2F%28e%5E%287r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "replace P from the 1st equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120411%2F%28e%5E%282r%29%29 ALIGN=MIDDLE  ALT=\"120411%2F%28e%5E%282r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*e^(7r) = 1083699<BR>\n" );
document.write( "Cancel the e^(2r)<BR>\n" );
document.write( "120411*e^(5r) = 1083699<BR>\n" );
document.write( "e^(5r) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1083699%2F120411 ALIGN=MIDDLE  ALT=\"1083699%2F120411\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Find the ln of both sides (ln(e)= 1)<BR>\n" );
document.write( "5r = 2.197<BR>\n" );
document.write( "r = .439 is the growth rate<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2.) How many bacteria were initially introduced to the Petri dish? (Round to the nearest bacteria).<BR>\n" );
document.write( "P = initial amt<BR>\n" );
document.write( "P * e^(2*.439) = 120411<BR>\n" );
document.write( "P * 2.40698 = 120411<BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120411%2F2.40698 ALIGN=MIDDLE  ALT=\"120411%2F2.40698\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = 50046 bacteria initially<BR>\n" );
document.write( ":<BR>\n" );
document.write( "3.) How many bacteria will there be after 12 hours? (Round to the nearest bacteria).<BR>\n" );
document.write( "A = 50046*e^(12*.439)<BR>\n" );
document.write( "A = 9,710,301 bacteria after 12 hrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "4.) How long does it take for the bacteria colony to reach 361233 bacteria? (round to 2 decimal places)<BR>\n" );
document.write( "50046*e^(.439t) = 361233<BR>\n" );
document.write( "e^(.439t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=361233%2F50046 ALIGN=MIDDLE  ALT=\"361233%2F50046\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "find the ln of both sides<BR>\n" );
document.write( ".439t = 1.9766<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.9766%2F.439 ALIGN=MIDDLE  ALT=\"1.9766%2F.439\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 4.50 hrs<BR>\n" );
document.write( "  </SPAN>\n" );
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