document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077994>Question 1077994</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<BR>\n" );
document.write( "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 few hours.<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 be the time taken for the quantity of medicine in the bloodstream to halve. By a process<BR>\n" );
document.write( "of guessing and checking, estimate the value of th (accurate to 3 significant figures).<BR>\n" );
document.write( "(d) Determine the exact value of th.<BR>\n" );
document.write( "(e) Show that the halving time is constant. That is, show that starting from an arbitrary time<BR>\n" );
document.write( "t = a, the quantity of medicine is halved after an additional time th.<BR>\n" );
document.write( "(f) Sketch a graph of the function over a 4 hour period since the injection.<BR>\n" );
document.write( "(g) The patient can receive a new injection when the quantity of medicine is less than 2% of the<BR>\n" );
document.write( "original dose. For simplicity, this time delay is measured in a whole number of hours. Determine<BR>\n" );
document.write( "the wait time. For medicinal safety, should we round up or down to the nearest hour?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692476 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=692476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q=AB%5Et ALIGN=MIDDLE  ALT=\"Q=AB%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.75=1%2AB%5E40 ALIGN=MIDDLE  ALT=\"0.75=1%2AB%5E40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, if starting amount were 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C0.75%29=log%2810%2C%28B%5E40%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C0.75%29=log%2810%2C%28B%5E40%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Alog%2810%2CB%29=log%2810%2C0.75%29 ALIGN=MIDDLE  ALT=\"40%2Alog%2810%2CB%29=log%2810%2C0.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2CB%29=log%2810%2C0.75%29%2F40 ALIGN=MIDDLE  ALT=\"log%2810%2CB%29=log%2810%2C0.75%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2CB%29=-0.00312347 ALIGN=MIDDLE  ALT=\"log%2810%2CB%29=-0.00312347\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28B=1.00722%29 ALIGN=MIDDLE  ALT=\"cross%28B=1.00722%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=0.9928 ALIGN=MIDDLE  ALT=\"B=0.9928\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----fixed\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28Q=A%2A%281.00722%29%5Et%29 ALIGN=MIDDLE  ALT=\"cross%28Q=A%2A%281.00722%29%5Et%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%28Q=A%280.9928%29%5Et%29 ALIGN=MIDDLE  ALT=\"highlight%28Q=A%280.9928%29%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bh%5D ALIGN=MIDDLE  ALT=\"t%5Bh%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Half-Life\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29=1%2A%280.9928%29%5Et ALIGN=MIDDLE  ALT=\"%281%2F2%29=1%2A%280.9928%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C0.9928%5Et%29=log%2810%2C1%2F2%29 ALIGN=MIDDLE  ALT=\"log%2810%2C0.9928%5Et%29=log%2810%2C1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Alog%2810%2C0.9928%29=log%281%2F2%29 ALIGN=MIDDLE  ALT=\"t%2Alog%2810%2C0.9928%29=log%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=log%2810%2C1%2F2%29%2Flog%2810%2C0.9928%29 ALIGN=MIDDLE  ALT=\"t=log%2810%2C1%2F2%29%2Flog%2810%2C0.9928%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-0.30103%29%2F%28-0.00312347%29 ALIGN=MIDDLE  ALT=\"t=%28-0.30103%29%2F%28-0.00312347%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t%5Bh%5D=96%29 ALIGN=MIDDLE  ALT=\"highlight%28t%5Bh%5D=96%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------96 minutes </SPAN>\n" );
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