document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=556207>Question 556207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have asked a question similar to this in the past, but its works still elude me...\r<BR>\n" );
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document.write( "A population of a colony of bacteria grows expodentially with time. At start of experiment there are 6000. 1 hr later there are 6500. How long before it reaches 9500. Need exact and numerical approximation... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362193 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=362193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A population of a colony of bacteria grows exponentially with time.<BR>\n" );
document.write( " At start of experiment there are 6000. 1 hr later there are 6500.<BR>\n" );
document.write( " How long before it reaches 9500. Need exact and numerical approximation...<BR>\n" );
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document.write( "Find k<BR>\n" );
document.write( "6000*(1+k) = 6500<BR>\n" );
document.write( "1 + k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500%2F6000 ALIGN=MIDDLE  ALT=\"6500%2F6000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1 + k = 1.0833<BR>\n" );
document.write( "k = 1.0833 - 1<BR>\n" );
document.write( "k = .0833<BR>\n" );
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document.write( "Find t<BR>\n" );
document.write( "6000*(1+.0833)^t = 9500<BR>\n" );
document.write( "1.0833^t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9500%2F6000 ALIGN=MIDDLE  ALT=\"9500%2F6000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1,0833^t = 1.5833<BR>\n" );
document.write( "t*ln(1.0833) = ln(1.5833)<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.5833%29%2Fln%281.0833%29 ALIGN=MIDDLE  ALT=\"ln%281.5833%29%2Fln%281.0833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 5.74 hrs to reach 9500 (from 6000)<BR>\n" );
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