document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032365>Question 1032365</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the quantity Q, in mg, of medicine in a patient’s bloodstream is decreasing by 25% each 40 minutes. Let us write Q = f(t), where t is in minutes since the injection of medicine. Suppose<BR>\n" );
document.write( "the injection contains 300 mg of medicine.<BR>\n" );
document.write( "(a) Construct a table of values for Q as a function of t over a 4 hour period.<BR>\n" );
document.write( "(b) Find a formula for f in the form A × B^t<BR>\n" );
document.write( ", or an equivalent form.<BR>\n" );
document.write( "(c) Let Th (h is just a little below T , i cant put it in the correct form here ) be the time taken for the quantity of medicine in the bloodstream to halve. Determine<BR>\n" );
document.write( "the value of th.<BR>\n" );
document.write( "(d) Show that the halving time is constant.<BR>\n" );
document.write( "(e) Sketch a graph of the function over a 4 hour period since the injection.<BR>\n" );
document.write( "(f) The patient can receive a new injection when the quantity of medicine is less than 2% of the original dose. For simplicity, this time delay is measured in a whole number of hours. Determine the wait time. For medical safety, should we round up or down to the nearest hour? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647021 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=647021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Loss of 25% every 40 minutes is the same as KEEPING 75% every 40 minutes.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28Q=A%2A%280.75%29%5Et%29 ALIGN=MIDDLE  ALT=\"highlight_green%28Q=A%2A%280.75%29%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You are interested among other questions, in the half-life, and you can use  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F40 ALIGN=MIDDLE  ALT=\"t%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "as the exponent.  NOW,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q=A%280.75%29%5E%28t%2F40%29 ALIGN=MIDDLE  ALT=\"Q=A%280.75%29%5E%28t%2F40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  uses t to count MINUTES, so the form of the<BR>\n" );
document.write( "equation is a little different.   Half life would be like so...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29=%280.75%29%5E%28t%2F40%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29=%280.75%29%5E%28t%2F40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Choosing natural log,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.75%5E%28t%2F40%29%29=ln%281%2F2%29 ALIGN=MIDDLE  ALT=\"ln%280.75%5E%28t%2F40%29%29=ln%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%2F40%29%2Aln%280.75%29=ln%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28t%2F40%29%2Aln%280.75%29=ln%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=40%2Aln%281%2F2%29%2Fln%280.75%29 ALIGN=MIDDLE  ALT=\"t=40%2Aln%281%2F2%29%2Fln%280.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=40%28ln%281%2F2%29%2Fln%283%2F4%29%29 ALIGN=MIDDLE  ALT=\"t=40%28ln%281%2F2%29%2Fln%283%2F4%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=t=40%280.69314%2F0.28768%29 ALIGN=MIDDLE  ALT=\"t=40%280.69314%2F0.28768%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=96.4%29 ALIGN=MIDDLE  ALT=\"highlight%28t=96.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------------half life in minutes.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );