document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171696>Question 1171696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Paracetamol is a drug used to treat mild to moderate pain and to reduce fever. It has a half-life in the body of 3 hours. Under a Doctor's care, patient N is given a dose of a certain paracetamol. Patient N asks the doctor for another same dose of this paracetamol. The doctor agrees to allow patient N to take dose once there is only 6.25% of the original dose remaining in the body. How long will patient N have to wait, before taking another dose of this paracetamol? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796601 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=796601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula for half life is:<BR>\n" );
document.write( "1/2 = (1 + r) ^ n<BR>\n" );
document.write( "when n = 3, the formula becomes:<BR>\n" );
document.write( "1/2 = (1 + r) ^ 3<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = (1/2) ^ (1/3) - 1 = -.206299474.<BR>\n" );
document.write( "that's your growth rate per time period.<BR>\n" );
document.write( "confirm by replacing r in the original equation to get:<BR>\n" );
document.write( "1/2 = (1 + r) ^ 3 becomes:<BR>\n" );
document.write( "1/2 = (1 - .206299474) ^ 3 = 1/2<BR>\n" );
document.write( "this confirms the value of r is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to find how long the patient has to wait for there to be only 6.25% of the original dose in his system, the the formula becomes.<BR>\n" );
document.write( ".0625 = 1 * (1 - .206299474) ^ n<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( ".0625 = (1 - .206299474) ^ n<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(.0625) = log((1-.206299474)^n)<BR>\n" );
document.write( "since log(x^n) = n * log(x), this becomes:<BR>\n" );
document.write( "log(.0625) = n * log(1 - .206299474)<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = log(.0625) / log(1 - .206299474) = 12.<BR>\n" );
document.write( "confirm by replacing n in the original equation to get:<BR>\n" );
document.write( ".0625 = (1 - .206299474) ^ n becomes:<BR>\n" );
document.write( ".0625 = (1 - .206299474) ^ 12 = .0625<BR>\n" );
document.write( "this confirms the value of n is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that the patient will have to wait 12 hours before taking another dose.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );