document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987202>Question 987202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE PLEASE HELP I can't seem to figure out how to do these four problems.\r<BR>\n" );
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document.write( "My kids’ bathtub is being drained. Since it is an ordinary tub, it can be modeled by the function  <BR>\n" );
document.write( "V(t) = -15t + 45 where V(t) is the volume of the tub in gallons and t is the time that has passed in minutes.\r<BR>\n" );
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document.write( "1.Based on the function V(t) = -15t + 45, when will the tub be half full?\r<BR>\n" );
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document.write( "2.What is the practical domain in this problem?  Use appropriate notation in your answer.\r<BR>\n" );
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document.write( "3.What is the practical range?  Use the appropriate notation in your answer.\r<BR>\n" );
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document.write( "4.My tub is a garden tub. When I drain it I can model the volume of water in it by <BR>\n" );
document.write( "v(T) = -20T + 50 where v(T) is the volume of the tub in gallons and T is the time that has passed <BR>\n" );
document.write( "in minutes.  Given all this, which tub drains faster, my kids’ tub, or mine? Explain your reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #607979 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=607979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> . <BR>\n" );
document.write( "1. When t=0, the tub has not yet started to drain:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%280%29=-15%280%29%2B45 ALIGN=MIDDLE  ALT=\"V%280%29=-15%280%29%2B45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%280%29=45 ALIGN=MIDDLE  ALT=\"V%280%29=45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The total volume of the tub is 45 gallons. <BR>\n" );
document.write( "The tub will be half full when V(t)=(1/2)(45gal)=22.5gal:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28t%29=-15t%2B45 ALIGN=MIDDLE  ALT=\"V%28t%29=-15t%2B45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.5=-15t%2B45 ALIGN=MIDDLE  ALT=\"22.5=-15t%2B45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 45 from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-22.5=-15t ALIGN=MIDDLE  ALT=\"-22.5=-15t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide each side by -15.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5=t ALIGN=MIDDLE  ALT=\"1.5=t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ANSWER: The tub will be half empty in 1.5 minutes.<BR>\n" );
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document.write( "2. Domain: [0,3] <BR>\n" );
document.write( "Since t is time, it is not less than zero. So 0<=t. <BR>\n" );
document.write( "If t>3, the volume is negative so t<=3.<BR>\n" );
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document.write( "3. Range: [0,45]<BR>\n" );
document.write( "V(t) is volume, cannot be less than zero: 0<+V(t)<BR>\n" );
document.write( "At t=0, the tub is full at 45 gallons, so: V(t)<=45 <BR>\n" );
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document.write( "4. Kid's tub, t when V(t)=0 is time to drain fully:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28t%29+=+-15t+%2B+45 ALIGN=MIDDLE  ALT=\"V%28t%29+=+-15t+%2B+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-15t%2B45 ALIGN=MIDDLE  ALT=\"0=-15t%2B45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-45=-15t ALIGN=MIDDLE  ALT=\"-45=-15t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=t ALIGN=MIDDLE  ALT=\"3=t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It takes 3 minutes to drain this tub completely.<BR>\n" );
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document.write( "For the garden tub when V(t)=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28t%29=-20t%2B50 ALIGN=MIDDLE  ALT=\"V%28t%29=-20t%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-20t%2B50 ALIGN=MIDDLE  ALT=\"0=-20t%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50=-20t ALIGN=MIDDLE  ALT=\"-50=-20t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5=t ALIGN=MIDDLE  ALT=\"2.5=t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It takes 2.5 minutes to completely drain the garden tub. <BR>\n" );
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document.write( "ANSWER: The garden tub drains faster.<BR>\n" );
document.write( "REASONING: The kid's tub drains 45 gal/3 min=15 gal/min.<BR>\n" );
document.write( "The garden tub drains 50 gal/2.5 min=20gal/min.<BR>\n" );
document.write( "The garden tub drains more water in less time.  \r<BR>\n" );
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