document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146036>Question 1146036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At A water tank is being filled by water being pumped into the tank at a volume given by the formula, P(t) = 112t +2000 gallons per minute, where t is in minutes.  At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula L(t) = 15t2 gallons per minute, where t is in minutes.  \r<BR>\n" );
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document.write( "The volume, V, of water in the tank at any minute, t, is the difference of the volume of the water being pumped into the tank and the volume of water leaking out of the tank.  Find the volume function, V(t).<BR>\n" );
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document.write( "The statement of the problem is incorrect.<br><BR>\n" );
document.write( "The difference between the two functions showing how fast water is being pumped in and how fast it is leaking out only tell you how the volume is changing as a function of time; it does NOT give you the volume as a function of time.<br><BR>\n" );
document.write( "So the function showing how the volume of water is changing (\"C(t)\") is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28t%29+=+P%28t%29-L%28t%29+=+%28112t+%2B2000%29-%2815t%5E2%29+=+-15t%5E2%2B112t%2B2000 ALIGN=MIDDLE  ALT=\"C%28t%29+=+P%28t%29-L%28t%29+=+%28112t+%2B2000%29-%2815t%5E2%29+=+-15t%5E2%2B112t%2B2000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the VOLUME function V(t) is the initial volume V(0) plus C(t).<br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "The volume function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28t%29+=+V%280%29-15t%5E2%2B112t%2B2000 ALIGN=MIDDLE  ALT=\"V%28t%29+=+V%280%29-15t%5E2%2B112t%2B2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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