document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192700>Question 1192700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume of water, v million cubic meters in a lake t ours after a storm is modelled by V = 2t(e^-t)+5\r<BR>\n" );
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document.write( "a. What is the initial volume of the lake and he maximum volume of the lake.<BR>\n" );
document.write( "b. When is the lake emptying the fastest. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824588 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of water, v million cubic meters in a lake t ours after a storm is modelled by V = 2t(e^-t)+5\r<BR>\n" );
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document.write( "a. What is the initial volume of the lake and he maximum volume of the lake.<BR>\n" );
document.write( "b. When is the lake emptying the fastest.<BR>\n" );
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document.write( "V(t) = 2t(e^-t)+5<BR>\n" );
document.write( "V(0) = 2*0 + 5 = 5 million cubic meters.<BR>\n" );
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document.write( "Find the 1st derivative:<BR>\n" );
document.write( "V'(t) = 2(e^-t) - 2t*e(^-t)<BR>\n" );
document.write( "Find the max of V'(t)<BR>\n" );
document.write( "V'(t) = 2(e^-t) - 2t*e(^-t) = 0<BR>\n" );
document.write( "2e^-t = 2t*e^-t<BR>\n" );
document.write( "t = 1 hour\r<BR>\n" );
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document.write( " </SPAN>\n" );
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