document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157132>Question 1157132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain culture of the bacterium Rhodobacter sphaeroides initially has 40 bacteria and is observed to double every 6 hours.<BR>\n" );
document.write( "(a) Find an exponential model <BR>\n" );
document.write( "n(t) = n02t/a<BR>\n" );
document.write( " for the number of bacteria in the culture after t hours.<BR>\n" );
document.write( "n(t) =___________\r<BR>\n" );
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document.write( "(b) Estimate the number of bacteria after 15 hours. (Round your answer to the nearest whole number.)<BR>\n" );
document.write( " ______bacteria\r<BR>\n" );
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document.write( "(c) After how many hours will the bacteria count reach 1 million? (Round your answer to one decimal place.)<BR>\n" );
document.write( "t = ________hr </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779954 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> n(t)=no (1+r)^x<BR>\n" );
document.write( "n(t)=40(1+r)^x<BR>\n" );
document.write( "80=40(1+r)^6<BR>\n" );
document.write( "2=(1+r)^6<BR>\n" );
document.write( "ln 2=6 ln (1+r)<BR>\n" );
document.write( "ln2/6=0.0155=1n(1+r)\r<BR>\n" );
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document.write( "raise to e power<BR>\n" );
document.write( "1.122=1+r<BR>\n" );
document.write( "r=12.2% growth rate per hour.\r<BR>\n" );
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document.write( "after t hours, n(t)=40(1.122)^t<BR>\n" );
document.write( "after 15 hours n(15)=40*5.622=224.88 or 225, start rounding at the end. 80 at 6 hours 160 at 12 and 320 at 18 so reasonable answer<BR>\n" );
document.write( "1000000=40(1.122)^t<BR>\n" );
document.write( "25000=1.122^t<BR>\n" );
document.write( "ln 25000=t ln 1.122<BR>\n" );
document.write( "divide through <BR>\n" );
document.write( "t=87.97 or 88.0 hours\r<BR>\n" );
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document.write( "rough check<BR>\n" );
document.write( "1 million / 40=25000<BR>\n" );
document.write( "2^14=16384<BR>\n" );
document.write( "2^15=32768\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );