document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=898295>Question 898295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to use the C(t) = Co e ^(-rt) formula?\r<BR>\n" );
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document.write( "Here is some background information\r<BR>\n" );
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document.write( "Exponential functions can be used to model the concentration of a drug in a patient's body. Suppose the concentration of Drug X in a patient's bloodstream is modeled by, \r<BR>\n" );
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document.write( "C (t) = C0 e - rt,\r<BR>\n" );
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document.write( "where C (t) represents the concentration at time t (in hours), C0 is the concentration of the drug in the blood immediately after injection, and r > 0 is a constant indicating the removal of the drug by the body through metabolism and/or excretion. The rate constant r has units of 1/time (1/hr). It is important to note that this model assumes that the blood concentration of the drug (C0 ) peaks immediately when the drug is injected.\r<BR>\n" );
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document.write( "the problem says \r<BR>\n" );
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document.write( " Round your answer to the nearest tenth and use the model C(t) = Co e^(-rt). If for drug x, r = 0.20 1/hr\r<BR>\n" );
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document.write( "a) how long after injection does it take for the concentration of a drug x to decrease to 35% of the initial level?\r<BR>\n" );
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document.write( "b) what can be said about the drug concentration in the body and the removal rate for this scenario. Use units of measure.\r<BR>\n" );
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document.write( "Any help would be really appreciated. I am very stuck on this problem \r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #544743 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=544743\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Round your answer to the nearest tenth and use the model C(t) = Co e^(-rt). If for drug x, r = 0.20 1/hr <BR>\n" );
document.write( "a) how long after injection does it take for the concentration of a drug x to decrease to 35% of the initial level? <BR>\n" );
document.write( "C(t) = Co e^(-rt)<BR>\n" );
document.write( "0.35 = e^(-0.2t)<BR>\n" );
document.write( "ln(0.35) = -0.2t<BR>\n" );
document.write( "t = -ln(0.35)/0.2<BR>\n" );
document.write( "t =~ 5.25 hours<BR>\n" );
document.write( "--> 5.3 hours<BR>\n" );
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document.write( "b) what can be said about the drug concentration in the body and the removal rate for this scenario. Use units of measure.<BR>\n" );
document.write( "The removal rate is dependent on the amount remaining, ie, the concentration.<BR>\n" );
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