document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374254>Question 374254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Water is leaking from a tank at a constant rate of 20% per hour. If yn denotes the amount of water at the beginning of the hour, in how many hours would Yn &#8804; y1/10? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266353 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266353\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I take this to mean the water left in the tank<BR>\n" );
document.write( "is less than or equal to 1/10 of the starting<BR>\n" );
document.write( "amount of water after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours<BR>\n" );
document.write( "after 1st hour: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+-+.2y%5B1%5D+=+.8y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D+-+.2y%5B1%5D+=+.8y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "after 2nd hour: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8y%5B1%5D+-+.2%2A.8y%5B1%5D+=+.8%5E2%2Ay%5B1%5D ALIGN=MIDDLE  ALT=\".8y%5B1%5D+-+.2%2A.8y%5B1%5D+=+.8%5E2%2Ay%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "after 3rd hour: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8%5E2%2Ay%5B1%5D+-+.2%2A.8%5E2%5B1%5D+=+.8%5E3%2Ay%5B1%5D ALIGN=MIDDLE  ALT=\".8%5E2%2Ay%5B1%5D+-+.2%2A.8%5E2%5B1%5D+=+.8%5E3%2Ay%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The pattern here is that after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours,<BR>\n" );
document.write( "the amount of water left in the tank is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8%5En%2Ay%5B1%5D ALIGN=MIDDLE  ALT=\".8%5En%2Ay%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The problem wants to know when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8%5En%2Ay%5B1%5D+%3C=+%281%2F10%29%2Ay%5B1%5D ALIGN=MIDDLE  ALT=\".8%5En%2Ay%5B1%5D+%3C=+%281%2F10%29%2Ay%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s cancel from both sides leaving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8%5En+%3C=+1%2F10 ALIGN=MIDDLE  ALT=\".8%5En+%3C=+1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A%28.8%5En%29+%3C=+1 ALIGN=MIDDLE  ALT=\"10%2A%28.8%5En%29+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8%5En+=+8%5En%2A10%5E%28-n%29 ALIGN=MIDDLE  ALT=\".8%5En+=+8%5En%2A10%5E%28-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A10%5E%28-n%29%2A+8%5En+%3C=+1 ALIGN=MIDDLE  ALT=\"10%2A10%5E%28-n%29%2A+8%5En+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%28-n+%2B+1%29%2A8%5En+%3C=+1 ALIGN=MIDDLE  ALT=\"10%5E%28-n+%2B+1%29%2A8%5En+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the log base 10 of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+n+%2B+n%2Alog%288%29+%3C=+0 ALIGN=MIDDLE  ALT=\"1+-+n+%2B+n%2Alog%288%29+%3C=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%28log%288%29+-+1%29+%3C=+-1 ALIGN=MIDDLE  ALT=\"n%2A%28log%288%29+-+1%29+%3C=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I need to multiply both sides by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which reverses the < sign<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E=+1%2F%281+-+log%288%29%29 ALIGN=MIDDLE  ALT=\"n+%3E=+1%2F%281+-+log%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E=+1%2F%281+-+.90309%29 ALIGN=MIDDLE  ALT=\"n+%3E=+1%2F%281+-+.90309%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E=+1%2F.09691 ALIGN=MIDDLE  ALT=\"n+%3E=+1%2F.09691\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E=+10.3189 ALIGN=MIDDLE  ALT=\"n+%3E=+10.3189\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E=+10 ALIGN=MIDDLE  ALT=\"n+%3E=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > in whole numbers<BR>\n" );
document.write( "The answer is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B10%5D+%3C=+%281%2F10%29%2Ay%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B10%5D+%3C=+%281%2F10%29%2Ay%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Unless I messed up- I think the approach is right\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );