document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072004>Question 1072004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem .<BR>\n" );
document.write( "A 2000-L tank is initially filled with a copper sulfate solution with a concentration of 60g/L . A copper sulfate solution with a concentration of 20g/L flows into the tank at rate of 8L/min . The thoroughly mixed solution is drained from the tank at rate 8L/min .<BR>\n" );
document.write( "A)write an initial value problem for the mass of the copper sulfate .<BR>\n" );
document.write( "B)Solve the initial value problem . Set up .\r<BR>\n" );
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document.write( "This is how i solved it but i might be 90% wrong .Please feel free to correct anything i did wrong .\r<BR>\n" );
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document.write( "Let y(t) be the amount of sulfate .<BR>\n" );
document.write( "y(0)=60<BR>\n" );
document.write( "dy/dt=(rate in)-(rate out)<BR>\n" );
document.write( "rate in =(20g/L)(8L/min)=160g/min<BR>\n" );
document.write( "rate out =y(t)g/2000L)(8L/min)=y(t)g/250min<BR>\n" );
document.write( "dy/dt=160-(y(t)/250)<BR>\n" );
document.write( "dy/dt=(40000-y(t))/250<BR>\n" );
document.write( "taking integral both side<BR>\n" );
document.write( "int(dy/40000-y)=int(dt/250)<BR>\n" );
document.write( "-ln(40000-y)=t/250+c<BR>\n" );
document.write( "since y(0)=60 , we have -ln39940=c<BR>\n" );
document.write( "-ln(40000-y)=t/250-ln39940<BR>\n" );
document.write( "since y(t)is continuous and y(0)=60 , so 40000-y(t) is positive . Thus 40000-y=40000-y<BR>\n" );
document.write( "y(t) 40000-39940e^(-t/250).\r<BR>\n" );
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document.write( "*Please any help will be very appreciate . Thank <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686930 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=686930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can't integrate both sides. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdt=160-%281%2F250%29y ALIGN=MIDDLE  ALT=\"dy%2Fdt=160-%281%2F250%29y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdt%2B%281%2F250%29y=160 ALIGN=MIDDLE  ALT=\"dy%2Fdt%2B%281%2F250%29y=160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "General solution,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ae%5E%28bt%29 ALIGN=MIDDLE  ALT=\"y=ae%5E%28bt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Particular solution,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=250%28160%29 ALIGN=MIDDLE  ALT=\"y=250%28160%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );