document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117420>Question 117420</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534954146/algebrahomeworkh>Fundamentals of Algebra and Trig</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am terrible with word problems and would like it if I could get some help with this one. Thanks\r<BR>\n" );
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document.write( "If the polution in lake Erie were stopped suddenly it has been estimated that the level y of pollutants would decrease according to the formula<BR>\n" );
document.write( " y= y0e ^(-0.3821t) (0 being the base) where t is the time in years and y0 is the pollutant level at which further pollution ceased. How many years would it take to clear 50% of the pollution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85429 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=85429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you started with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D ALIGN=MIDDLE  ALT=\"y%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > amount of<BR>\n" );
document.write( "pollution, and reduced it by 50%, you'd have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5%2Ay%5B0%5D ALIGN=MIDDLE  ALT=\".5%2Ay%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > left, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+.5%2Ay%5B0%5D ALIGN=MIDDLE  ALT=\"y+=+.5%2Ay%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+y%5B0%5D%2Ae%5E%28-.3821%2At%29 ALIGN=MIDDLE  ALT=\"y+=+y%5B0%5D%2Ae%5E%28-.3821%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5%2Ay%5B0%5D+=+y%5B0%5D%2Ae%5E%28-.3821%2At%29 ALIGN=MIDDLE  ALT=\".5%2Ay%5B0%5D+=+y%5B0%5D%2Ae%5E%28-.3821%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D ALIGN=MIDDLE  ALT=\"y%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5+=+e%5E%28-.3821%2At%29 ALIGN=MIDDLE  ALT=\".5+=+e%5E%28-.3821%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the ln (log to the base e) of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.5%29+=+ln%28e%5E%28-.3821%2At%29%29 ALIGN=MIDDLE  ALT=\"ln%28.5%29+=+ln%28e%5E%28-.3821%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The trick is to READ the right side correctly. What does it say,exactly?<BR>\n" );
document.write( "It says \"What log to the base e gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-.3821%2At%29 ALIGN=MIDDLE  ALT=\"e%5E%28-.3821%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "It's very obviously <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.3821%2At ALIGN=MIDDLE  ALT=\"-.3821%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.5%29+=+-.3821%2At ALIGN=MIDDLE  ALT=\"ln%28.5%29+=+-.3821%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use a calculator to find the left side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.69315+=+-.3821%2At ALIGN=MIDDLE  ALT=\"-.69315+=+-.3821%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.814 ALIGN=MIDDLE  ALT=\"t+=+1.814\"   DISABLED_style= \"max-width:90%; height:auto;\" >years<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.814 ALIGN=MIDDLE  ALT=\".814\"   DISABLED_style= \"max-width:90%; height:auto;\" >years X <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > months/year = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.768 ALIGN=MIDDLE  ALT=\"9.768\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So far its<BR>\n" );
document.write( "1 year 9.768 months<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.768 ALIGN=MIDDLE  ALT=\".768\"   DISABLED_style= \"max-width:90%; height:auto;\" >months X <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" >days/month = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23.04 ALIGN=MIDDLE  ALT=\"23.04\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the answer is<BR>\n" );
document.write( "1 year, 9 months, 23 days approximately <BR>\n" );
document.write( "check answer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5+=+e%5E%28-.3821%2At%29 ALIGN=MIDDLE  ALT=\".5+=+e%5E%28-.3821%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5+=+e%5E%28-.3821%2A1.814%29 ALIGN=MIDDLE  ALT=\".5+=+e%5E%28-.3821%2A1.814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5+=+e%5E-.6931 ALIGN=MIDDLE  ALT=\".5+=+e%5E-.6931\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5+=+.50000889 ALIGN=MIDDLE  ALT=\".5+=+.50000889\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is close enough </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );