document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208076>Question 1208076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The concentration C of a medication in the bloodstream t hours after being administered is modeled by the function\r<BR>\n" );
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document.write( "C(t) = -0.002t^4 + 0.039t^3 - 0.285t^2 + 0.766t + 0.085\r<BR>\n" );
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document.write( "A. After how may hours will the concentration be highest?\r<BR>\n" );
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document.write( "B. A woman nursing a child must wait until the concentration is below 0.5 before she can feed him. After taking the medication, how long must she wait before feeding her child? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846228 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part A\r<BR>\n" );
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document.write( "I'll use x in place of t.<BR>\n" );
document.write( "Type <font color=blue>y = -0.002x^4+0.039x^3-0.285x^2+0.766x+0.085</font> into Desmos.\r<BR>\n" );
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document.write( "Here is the link<BR>\n" );
document.write( "https://www.desmos.com/calculator\r<BR>\n" );
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document.write( "Notice if you clicked on the curve, a few points show up.<BR>\n" );
document.write( "Click on the highest point to display the coordinates (2.1603, 0.75936)<BR>\n" );
document.write( "Both of those decimal values are approximate.<BR>\n" );
document.write( "Therefore, the max concentration is around 0.75936 which happens at the timestamp of roughly 2.1603 hours.\r<BR>\n" );
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document.write( "--------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "Revisit the Desmos page where you typed in <font color=blue>y = -0.002x^4+0.039x^3-0.285x^2+0.766x+0.085</font>\r<BR>\n" );
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document.write( "In the box below that, type in <font color=blue>y = 0.5</font><BR>\n" );
document.write( "A horizontal line will show up.<BR>\n" );
document.write( "This line intersects the curve in two locations.<BR>\n" );
document.write( "Click the points of intersection to have their coordinates show up.<BR>\n" );
document.write( "You should see (0.71326, 0.5) and (4.46534, 0.5)<BR>\n" );
document.write( "The 0.5's are exact but the other decimal values are approximate.\r<BR>\n" );
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document.write( "When 0 < x < 0.71326, the concentration of the medication is between 0 and 0.5<BR>\n" );
document.write( "This is the first window of opportunity the woman has to feed her child.<BR>\n" );
document.write( "If she must wait for the concentration to go past 0.5 and then come down again, then this window must be ignored.\r<BR>\n" );
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document.write( "When 0.71326 < x < 4.46534, the concentration is above 0.5\r<BR>\n" );
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document.write( "After the 4.46534 hour marker (approximate), the concentration will dip below 0.5<BR>\n" );
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