document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102754>Question 1102754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3. Initially a tank contains 10,000 liters of liquid. At the time t=0 minutes a tap is opened, and liquid then flows out of the tank. The volume of liquid, V liters, which remains in the tank after t minutes is given by V=10,000(0.933)^t. <BR>\n" );
document.write( "a. Find out how much liquid is in the tank after 5 minutes. <BR>\n" );
document.write( "b. Find out how long, to the nearest second, it takes for half of the initial amount of liquid to flow out of the tank. <BR>\n" );
document.write( "c. The tank is regarded as effectively empty when 95% of the liquid has flowed out. Show that this takes almost three-quarters of an hour. <BR>\n" );
document.write( "d. (i) Find the value of 10,000 - V when t=0.001 minutes. <BR>\n" );
document.write( "(ii) Hence, or otherwise, estimate the initial flow rate of the liquid.<BR>\n" );
document.write( "Give your answer in liters per minute, correct to two significant figures. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717489 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=717489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3. Initially a tank contains 10,000 liters of liquid. At the time t=0 minutes a tap is opened, and liquid then flows out of the tank. The volume of liquid, V liters, which remains in the tank after t minutes is given by V=10,000(0.933)^t. <BR>\n" );
document.write( "a. Find out how much liquid is in the tank after 5 minutes. <BR>\n" );
document.write( "Sub 5 for t, calculate.<BR>\n" );
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document.write( "b. Find out how long, to the nearest second, it takes for half of the initial amount of liquid to flow out of the tank. <BR>\n" );
document.write( "V=10,000(0.933)^t = 5000<BR>\n" );
document.write( "Solve for t.<BR>\n" );
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document.write( "c. The tank is regarded as effectively empty when 95% of the liquid has flowed out. Show that this takes almost three-quarters of an hour. <BR>\n" );
document.write( "V=10,000(0.933)^t = 500<BR>\n" );
document.write( "Solve for t.<BR>\n" );
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document.write( "d. (i) Find the value of 10,000 - V when t=0.001 minutes<BR>\n" );
document.write( "Sub 0.001 for t.<BR>\n" );
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document.write( "(ii) Hence, or otherwise, estimate the initial flow rate of the liquid.<BR>\n" );
document.write( "Give your answer in liters per minute, correct to two significant figures.<BR>\n" );
document.write( "The result of d. (i) above is a good estimate.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );