document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002149>Question 1002149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a colony of bacteria increases exponentially with time. If the population starts with 8000 bacteria and 4 hours later the population is 10000...\r<BR>\n" );
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document.write( "a.) when will the population be 12000?<BR>\n" );
document.write( "b.) what is the doubling time?<BR>\n" );
document.write( "c.) what will the population be after 10 hours? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619189 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=619189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In general, exponential growth takes the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28t%29+=+Ao%28e%5E%28kt%29%29 ALIGN=MIDDLE  ALT=\"A%28t%29+=+Ao%28e%5E%28kt%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's plug in to find k...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000=8000%2Ae%5E%284k%29 ALIGN=MIDDLE  ALT=\"10000=8000%2Ae%5E%284k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.25+=+e%5E%284k%29 ALIGN=MIDDLE  ALT=\"1.25+=+e%5E%284k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.25%29+=+4k ALIGN=MIDDLE  ALT=\"ln%281.25%29+=+4k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k = ln(1.25)/4 = .05579<BR>\n" );
document.write( "Now plug that into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28t%29+=+Ao%28e%5E%28kt%29%29 ALIGN=MIDDLE  ALT=\"A%28t%29+=+Ao%28e%5E%28kt%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28t%29+=+Ao%28e%5E%28.05579%2At%29%29 ALIGN=MIDDLE  ALT=\"A%28t%29+=+Ao%28e%5E%28.05579%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and for your case<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28t%29+=+8000%2A%28e%5E%28.05579%2At%29%29 ALIGN=MIDDLE  ALT=\"A%28t%29+=+8000%2A%28e%5E%28.05579%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now plug in 12000 for A(t) to find t for part a,<BR>\n" );
document.write( "plug in 16000 for A(t) to find t for part b,<BR>\n" );
document.write( "and plug in 10 for t to find A(t)for part c.<BR>\n" );
document.write( " </SPAN>\n" );
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