document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196943>Question 1196943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The remaining concentration of a drug in a person’s bloodstream is modeled by the relation ​᠎​​᠎​C=C0(1/2)^t/8, where C is the remaining concentration of the drug in the bloodstream in milligrams per milliliter of blood, C0 is the initial concentration, and t is the time, in hours, that the drug is in the bloodstream.\r<BR>\n" );
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document.write( "What is the half-life of this drug?\r<BR>\n" );
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document.write( "A nurse gave a patient this drug, which was 20 mg/ml. What is the concentration of this drug in 3.5 hours? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829987 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=829987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think your equation is C = C0 * (1/2) ^ (t/8)<BR>\n" );
document.write( "half life formula would be .5 = (1/2) ^ (t/8)<BR>\n" );
document.write( "take the log of both sides of this equation to get:<BR>\n" );
document.write( "log(.5) = log((1/2)^(t/8))<BR>\n" );
document.write( "by log rules, this becomes:<BR>\n" );
document.write( "log(.5) = t/8 * log(1/2)<BR>\n" );
document.write( "solve for t/8 to get:<BR>\n" );
document.write( "t/8 = log(.5) / log(.5) = 1<BR>\n" );
document.write( "solve for t to get:<BR>\n" );
document.write( "t = 8<BR>\n" );
document.write( "half life of C is equal ti 8 hours.<BR>\n" );
document.write( "confirm by replacing t with 8 to get:<BR>\n" );
document.write( "C = (1/2) ^ (8/8) = (1/2) ^ 1 = (1/2)<BR>\n" );
document.write( "if the initial dose was 20, then the formula becomes:<BR>\n" );
document.write( "C = 20 * (1/2) ^ (3.5/8) = 14.76826146.<BR>\n" );
document.write( "that should be your solution.<BR>\n" );
document.write( "the equation can be graphed as shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/100602.jpg\"><BR>\n" );
document.write( "from the graph you can see that the initial concentration is 20 at x = 0 and the half life is 10 at x = 8 and the amount remaining at x = 3.5 is 14.768.<BR>\n" );
document.write( "x is the number of hours.<BR>\n" );
document.write( "y is the amount of drug remaining in the system.<BR>\n" );
document.write( " </SPAN>\n" );
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