document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=898920>Question 898920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Drug Concentration. When a pharmaceutical drug is injected into the bloodstream, it's concentration at time t can be approximated by C(t) = C0(e)^-kt, where C0 is is the concentration at t = 0. Suppose the drug is ineffective below a concentration C1 and harmful above concentration C2. Then it can be shown that the drug should be given at intervals of the time T. Where T = (1/k)ln(C2/C1).\r<BR>\n" );
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document.write( "A certain drug is harmful at a concentration five times the concentration below which it is ineffective. At noon an injection of the drug result in a concentration of 2 mg per liter of blood. Three hours later the concentration is down to 1 mg per liter. How often should the drug be given? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #545045 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=545045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"At noon an injection...\" gives the data to find k in the <i>first</i> equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2FCo=e%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"C%2FCo=e%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28C%2FCo%29=-kt%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%28C%2FCo%29=-kt%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28C%2FCo%29=-kt ALIGN=MIDDLE  ALT=\"ln%28C%2FCo%29=-kt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-%281%2Ft%29ln%28C%2FCo%29 ALIGN=MIDDLE  ALT=\"k=-%281%2Ft%29ln%28C%2FCo%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_green%28k=%281%2Ft%29ln%28Co%2FC%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=%281%2Ft%29ln%28Co%2FC%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The variable choices are slightly different than yours.<BR>\n" );
document.write( "The data in the rest of that sentence and the next one put into this formula makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F3%29ln%282%29 ALIGN=MIDDLE  ALT=\"k=%281%2F3%29ln%282%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_green%28k=0.231%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=0.231%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Knowing the value for k allows you to find the value for T, the time interval between effective and harmful.  Now, using YOUR choice of variables, C2=5*C and C1=C in this case for some constant C.  This gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=%281%2Fk%29ln%285%29 ALIGN=MIDDLE  ALT=\"T=%281%2Fk%29ln%285%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=%281%2F0.231%29ln%285%29 ALIGN=MIDDLE  ALT=\"T=%281%2F0.231%29ln%285%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=6.97%29 ALIGN=MIDDLE  ALT=\"highlight%28T=6.97%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, not sure if to the nearest hour might be best or not; but this could be stated T is 6 hours and 58 minutes. </SPAN>\n" );
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