document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150694>Question 150694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello E-Instructors :)\r<BR>\n" );
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document.write( "Would someone kindly show me how to solve this problem correctly? \r<BR>\n" );
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document.write( "Problem: The level of a prescription drug in the human body over time can be found using the formula: <BR>\n" );
document.write( "L= ___D___<BR>\n" );
document.write( "''''''''1-(1/2)^n/H  \r<BR>\n" );
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document.write( "where D is the amount taken every 'n' hours and H  is the drug's half-life in hours. <BR>\n" );
document.write( "(''''These marks are merely spacers and not intended to be part of the equation).\r<BR>\n" );
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document.write( "1. If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken <BR>\n" );
document.write( "   every 24 hours, then to what level does the drug build up over time?\r<BR>\n" );
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document.write( "   So far I think that the formula may look like this: <BR>\n" );
document.write( "2.5 = ___24________<BR>\n" );
document.write( "'''''''''''''1-(1/2)^24/14\r<BR>\n" );
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document.write( "   Then maybe this:  <BR>\n" );
document.write( "2.5 = ___24____<BR>\n" );
document.write( "'''''''''''''0.3047534\r<BR>\n" );
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document.write( "2.5 = 69.057991    \r<BR>\n" );
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document.write( "Then, I don't know what to do next or if what I've done is even close to being right. :P\r<BR>\n" );
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document.write( "               <BR>\n" );
document.write( "2. If a doctor wants the level of Lorazepam to build up to a level <BR>\n" );
document.write( "   of 5.58 milligrams in a patient taking 2.5 milligram doses, then how <BR>\n" );
document.write( "   often should the doses be taken?\r<BR>\n" );
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document.write( "   I'm completely in the dark about this one.\r<BR>\n" );
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document.write( "3. What is the difference between taking 2.5 milligram of Lorazepam <BR>\n" );
document.write( "   every 12 hours and taking 5 milligrams every 24 hours? \r<BR>\n" );
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document.write( "   This one, I might subtract results from these two equations:<BR>\n" );
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document.write( "2.5 = ___12_________                   <BR>\n" );
document.write( "''''''''''''1-(1/2)^12/14     <BR>\n" );
document.write( "from<BR>\n" );
document.write( "5 = ___24_______<BR>\n" );
document.write( "''''''''''1-(1/2)^24/14<BR>\n" );
document.write( "   <BR>\n" );
document.write( "   Well, that would be after I have learned how to solve the first question <BR>\n" );
document.write( "   correctly. ;)\r<BR>\n" );
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document.write( "Thank you so much for sharing your valuable knowledge with a mathematically challenged damsel like myself.\r<BR>\n" );
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document.write( "Grateful,<BR>\n" );
document.write( "J.   ;) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110636 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%28D%2F%281-%28%281%2F2%29%5E%28n%2FH%29%29%29%29 ALIGN=MIDDLE  ALT=\"L=%28D%2F%281-%28%281%2F2%29%5E%28n%2FH%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > I assume that this is the formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%282.5%2F%281-%28%281%2F2%29%5E%2824%2F14%29%29%29%29 ALIGN=MIDDLE  ALT=\"L=%282.5%2F%281-%28%281%2F2%29%5E%2824%2F14%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%282.5%2F%281-.304753%29%29 ALIGN=MIDDLE  ALT=\"L=%282.5%2F%281-.304753%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=2.5%2F.695247 ALIGN=MIDDLE  ALT=\"L=2.5%2F.695247\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "L=3.59585 mg<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.58=%282.5%2F%281-%28%281%2F2%29%5E%28n%2F14%29%29%29%29 ALIGN=MIDDLE  ALT=\"5.58=%282.5%2F%281-%28%281%2F2%29%5E%28n%2F14%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Let x=1-((1/2)^(n/14))<BR>\n" );
document.write( "5.58=2.5/x <BR>\n" );
document.write( "x=2.5/5.58<BR>\n" );
document.write( "x=.448029<BR>\n" );
document.write( "Let y=(1/2)^(n/14)<BR>\n" );
document.write( "1-y=.448029<BR>\n" );
document.write( "-y=.448029-1<BR>\n" );
document.write( "y=1-.448029<BR>\n" );
document.write( "y=.551971<BR>\n" );
document.write( "Let z=n/14<BR>\n" );
document.write( ".5^z=.551971<BR>\n" );
document.write( "log[.5](.5^z)=log[.5](.551971)<BR>\n" );
document.write( "z=log[.5](.551971)<BR>\n" );
document.write( "log[.5](.551971)=log[10](.551971)/log[10](.5)=.857336<BR>\n" );
document.write( "n/14=.857336<BR>\n" );
document.write( "n=14*.857336<BR>\n" );
document.write( "=12.0027 hrs<BR>\n" );
document.write( "So 2.5 mg must be given every 12 hrs.<BR>\n" );
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document.write( "3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%285%2F%281-%28%281%2F2%29%5E%2812%2F14%29%29%29%29 ALIGN=MIDDLE  ALT=\"L=%285%2F%281-%28%281%2F2%29%5E%2812%2F14%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "L=11.1618 mg<BR>\n" );
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document.write( "Ed\r<BR>\n" );
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document.write( " </SPAN>\n" );
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