document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1004915>Question 1004915</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( "PLEASE HELP ME THIS IS REALLY IMPORTANT FOR ME TO UNDERSTAND, THANK YOU!!!!!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621283 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) ln(N2/N1) = k(t2-t1)<BR>\n" );
document.write( "where N1, N2 are bacteria counts at times t1 and t2, and k is the growth rate<BR>\n" );
document.write( "ln(1083699 / 102411) = k(7-2)<BR>\n" );
document.write( "2.359141339 = 5k<BR>\n" );
document.write( "k = 0.471828268 approx 0.472<BR>\n" );
document.write( "the growth rate k is 0.472 hour^-1<BR>\n" );
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document.write( "2) t1 = 0<BR>\n" );
document.write( "ln(102411/N1) = 0.472(2-0)<BR>\n" );
document.write( "ln(102411/N1) = 0.944<BR>\n" );
document.write( "use definition of natural log<BR>\n" );
document.write( "102411/N1 = e^0.944<BR>\n" );
document.write( "N1 = 102411 / e^0.944 = 39844.888514675<BR>\n" );
document.write( "N1 = 39845 bacteria's<BR>\n" );
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document.write( "3) ln(N2/39845) = 0.472(12-0)<BR>\n" );
document.write( "ln(N2/39845) = 5.664<BR>\n" );
document.write( "N2/39845 = e^5.664<BR>\n" );
document.write( "N2 = 39845 * e^5.664 = 11487295.055974431<BR>\n" );
document.write( "N2 = 11487295 bacteria's<BR>\n" );
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document.write( "4) ln(361233/39845) = 0.472(t2-0)<BR>\n" );
document.write( "2.204526253 = t2(0.472)<BR>\n" );
document.write( "t2 = 4.670606467<BR>\n" );
document.write( "t2 = 4.67 hours<BR>\n" );
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