document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233600>Question 233600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain type of skin wound heals according to the function given by N(t)= N0e-0.125t , where N is the number of cm2 of unhealed skin t days after the injury, and N0 is the number of cm2  of the original wound. How long, to the nearest day, will it take for 75% of the wound to heal?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Please see below for further break downs\r<BR>\n" );
document.write( "\n" );
document.write( "N0= The 0 is slightly lower than the N<BR>\n" );
document.write( "-0.125t= It is squared to the N0e<BR>\n" );
document.write( "cm2= the 2 is squared here </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172415 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=172415\">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=N%5Bt%5D=+N%5B0%5D%2Ae%5E%28-0.125%2At%29 ALIGN=MIDDLE  ALT=\"N%5Bt%5D=+N%5B0%5D%2Ae%5E%28-0.125%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is what I believe your formula looks like after putting it through algebra.com formula generator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Just put three { in front and three } in back of the formula to see what algebra.com formula generator will make your formula look like.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "formula is: N[t]= N[0]*e^(-0.125*t)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Algebra.com formula generator makes it look like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5Bt%5D=+N%5B0%5D%2Ae%5E%28-0.125%2At%29 ALIGN=MIDDLE  ALT=\"N%5Bt%5D=+N%5B0%5D%2Ae%5E%28-0.125%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Anyway, your answer looks like it is 11 days to the nearest integer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The full answer shows up as 11.09035489\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's how it works:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "N[t] is what you are looking for.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you want to know how long it will take for 75% of the wound to heal, then you need to translate that into the percent of the wound that didn't heal which would make that 25%, because the formula is set up to show you the amount of skin remaining to be healed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you allow the original wound to be 1 square cm, then 25% of that would be .25 square cm. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "N[0] would be 1<BR>\n" );
document.write( "N[t] would be .25 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your formula of:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "N[t]= N[0]*e^(-0.125*t) would become:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".25 = 1*e^(-0.125*t)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".25 = e^(-0.125*t)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take the natural log of both sides to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ln(.25) = ln(e^(-0.125*t))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ln(.25) = -.125*t*ln(e)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since ln(e) = 1, this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ln(.25) = -.125*t\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides by -.125 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t = ln(.25)/(-.125)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for t to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t = 11.09035489\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I confirmed the answer is good by plugging into the original equation and solving.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );