document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190620>Question 190620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need your help on the following word problem:<BR>\n" );
document.write( "Given a starting population of 100 bacteria, the formula b=100(2^t) can be used to find the number of bacteria, \"b\", after \"t\" periods of time. If each period is 15 minutes long, how many minutes will it take for the population of bacteria to reach 51,200? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143092 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=143092\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=100%282%5Et%29 ALIGN=MIDDLE  ALT=\"b=100%282%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51200=100%282%5Et%29 ALIGN=MIDDLE  ALT=\"51200=100%282%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=51200 ALIGN=MIDDLE  ALT=\"b=51200\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the given bacteria population)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512=2%5Et ALIGN=MIDDLE  ALT=\"512=2%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 100.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28512%29%29=log%2810%2C%282%5Et%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28512%29%29=log%2810%2C%282%5Et%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log base 10 of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28512%29%29=t%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28512%29%29=t%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite right side using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28512%29%29%2Flog%2810%2C%282%29%29=t ALIGN=MIDDLE  ALT=\"log%2810%2C%28512%29%29%2Flog%2810%2C%282%29%29=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28512%29%29=t ALIGN=MIDDLE  ALT=\"log%282%2C%28512%29%29=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the change of base formula to rewrite the left side\r<BR>\n" );
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document.write( "Note: Remember the change of base formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=log%282%2C%28512%29%29 ALIGN=MIDDLE  ALT=\"t=log%282%2C%28512%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=9 ALIGN=MIDDLE  ALT=\"t=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the log base 2 of 512 to get 9\r<BR>\n" );
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document.write( "Note: \r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E9=512 ALIGN=MIDDLE  ALT=\"2%5E9=512\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28512%29%29=9 ALIGN=MIDDLE  ALT=\"log%282%2C%28512%29%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=9 ALIGN=MIDDLE  ALT=\"t=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that it will take 9 minutes for the population to reach 51,200 </SPAN>\n" );
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