document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025358>Question 1025358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A drug is administered to a patient and the concentration of the drug in the bloodstream is monitored. At time t &#8805; 0 (in hours since giving the drug), the concentration (in mg/L) is given by \r<BR>\n" );
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document.write( "c (t) = 5t/(t^2+1)\r<BR>\n" );
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document.write( "Graph the function c(t) <BR>\n" );
document.write( " What is the highest concentration of the drug that is reached in the   patient’s bloodstream?<BR>\n" );
document.write( "What happens to the drug concentration after a long period of time?<BR>\n" );
document.write( "How long does it take for the concentration to drop below 0.3 mg/L? \r<BR>\n" );
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document.write( "I need to know how to get each part a-d like the breakdown so I can understand please. <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 #640720 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=640720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%28t%29+=%285t%29%2F%28t%5E2%2B1%29+ ALIGN=MIDDLE  ALT=\"c%28t%29+=%285t%29%2F%28t%5E2%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+0%2C+8%2C+-8%2C+8%2C%285x%29%2F%28x%5E2%2B1%29%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+0%2C+8%2C+-8%2C+8%2C%285x%29%2F%28x%5E2%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b.  c'(t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285t+-+5t%5E2%29%2F%28t%5E2%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%285t+-+5t%5E2%29%2F%28t%5E2%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Setting this derivative to zero to get the extreme values, we get t = 0, 1.  Incidentally an absolute maximum exists at t = 1.  ( c(1) = 2.5 mg/L.)\r<BR>\n" );
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document.write( "c.  As <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-%3Einfinity ALIGN=MIDDLE  ALT=\"t-%3Einfinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%28t%29-%3E0 ALIGN=MIDDLE  ALT=\"c%28t%29-%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and so the drug concentration disappears over a long period of time.\r<BR>\n" );
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document.write( "d. You have to find the solution to the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285t%29%2F%28t%5E2%2B1%29+=+0.3 ALIGN=MIDDLE  ALT=\"%285t%29%2F%28t%5E2%2B1%29+=+0.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or equivalently, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3t%5E2+-+50t%2B3+=+0 ALIGN=MIDDLE  ALT=\"3t%5E2+-+50t%2B3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  (Use the quadratic formula.) </SPAN>\n" );
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