document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192675>Question 1192675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm getting stuck, so please I need a volunteer to help me<BR>\n" );
document.write( "here is the problem\r<BR>\n" );
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document.write( "For  surgeries  and  serious  injuries, anesthesiologists  are  responsible  for administering  anesthesia.  If  correct dosages  are  not  given  and  monitored, it  is possible  patients  may wake  up during a  procedure.  Avoiding  this  disaster  takes  analysis  of  an anesthesia’s concentration in the bloodstream. When  a  concentration  of  an  anesthesia  is  below 0.1 mg/L, it is no longer effective. In these two cases, you must use rational functions to model the anesthesia’s concentration in the bloodstream and determine when the patient may wake up.<BR>\n" );
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document.write( "Given a model for this patient’s concentration over time, complete the table with useful times or amounts. Use the model to determine when they may wake up.  Model y =2.8x/0.4x^2+ 1.3\r<BR>\n" );
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document.write( "Fill in the table with their correct value<BR>\n" );
document.write( "The first column represents the x values and the second column represents the y values<BR>\n" );
document.write( "Minutes Since Dose(x)                      Concentration in mg/L (y) <BR>\n" );
document.write( "                5 →                                       ...<BR>\n" );
document.write( "               10 →                                       ...<BR>\n" );
document.write( "               20 →                                       ...<BR>\n" );
document.write( "               30 →                                       ... <BR>\n" );
document.write( "               60 →                                       ...<BR>\n" );
document.write( "               ... →                                      0.4<BR>\n" );
document.write( "               ... →                                     0.2<BR>\n" );
document.write( "               ... →                                     0.1<BR>\n" );
document.write( "               ... →                                      0.01\r<BR>\n" );
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document.write( "1)Based on the model, when will the patient wake up?\r<BR>\n" );
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document.write( "2)If  the  procedure  lasts  approximately  1  hour  and  thirty  minutes,  will  additional  anesthesia  be required? \r<BR>\n" );
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document.write( "3)Can  you  determine  the  maximum  amount  of concentration  that  the  patient  had  in  their bloodstream? If it is over 2 mg/L, then it could be dangerous.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824744 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am assuming it is y=(2.8x)/(0.4x^2+1.3).<BR>\n" );
document.write( "x=5, y=14/(10+1.3)=14/11.3=1.24<BR>\n" );
document.write( "x=10, y=28/41.3=0.68<BR>\n" );
document.write( "x=20, y=56/161.3=0.35<BR>\n" );
document.write( "x=30, y=84/361.3=0.23<BR>\n" );
document.write( "x=60, y=168/1441.3=0.117<BR>\n" );
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document.write( "y=0.4=(2.8x)/(0.4x^2+1.3)<BR>\n" );
document.write( "0.16x^2+0.52=2.8x<BR>\n" );
document.write( "0.16x^2-2.8x+0.52=0<BR>\n" );
document.write( "16x^2-280x+52=0; 4x^2-70x+13=0<BR>\n" );
document.write( "x=17.3 min<BR>\n" );
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document.write( "y=0.2<BR>\n" );
document.write( "0.08x^2+0.26=2.8x<BR>\n" );
document.write( "0.08x^2-2.8x+0.26=0<BR>\n" );
document.write( "8x^2-280x+26=0; 4x^2-140x+13=0<BR>\n" );
document.write( "x=34.91 min<BR>\n" );
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document.write( "y=0.1<BR>\n" );
document.write( "0.04x^2+0.13=2.8x<BR>\n" );
document.write( "0.04x^-2.8x+0.13=0<BR>\n" );
document.write( "4x^2-280x+13=0<BR>\n" );
document.write( "x=70 min.<BR>\n" );
document.write( "An hour and a half would be too long. The minimum is reached in 1h10m<BR>\n" );
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document.write( "y=0.01<BR>\n" );
document.write( "0.004x^2-2.8x+0.013=0, 695 minutes\r<BR>\n" );
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document.write( "Substitute 2 for y \r<BR>\n" );
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document.write( "2=(2.8x)/(0.4x^2+1.3)<BR>\n" );
document.write( "0.8x^2+2.6=2.8x<BR>\n" );
document.write( "0.8x^2-2.8x+2.6=0<BR>\n" );
document.write( "8x^2-28x+26=0<BR>\n" );
document.write( "4x^2-7x+13=0, and this has complex roots, so it does not reach 2 mg/l\r<BR>\n" );
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document.write( "Take the derivative and it is y'=(0.4x^2+1.3)*2.8-(2.8x)(0.8x)/(0.4x^2+1.3)^2<BR>\n" );
document.write( "set y'=0 and multiply through by the denominator, which disappears<BR>\n" );
document.write( "so 1.12x^2+3.64=2.24x^2 and 1.12x^2=3.64 and x=1.80 min maximum\r<BR>\n" );
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document.write( "The horizontal lines are y=0.1,0.2,0.4,0.6,0.8 mg/l<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C100%2C-2%2C2%2C0.1%2C0.2%2C0.4%2C0.6%2C0.8%2C%282.8x%29%2F%280.4x%5E2%2B1.3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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