document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73053>Question 73053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have only 3 questions like this\r<BR>\n" );
document.write( "\n" );
document.write( "The amount of a radioactive tracer remaining after t days is given by A = AO e-0.18t, where A0 is the starting amount at the beginning of the time period. How much should be acquired now to have 40 grams remaining after 3 days?\r<BR>\n" );
document.write( "\n" );
document.write( "47.9\r<BR>\n" );
document.write( "\n" );
document.write( "48.8\r<BR>\n" );
document.write( "\n" );
document.write( "61.6\r<BR>\n" );
document.write( "\n" );
document.write( "68.6\r<BR>\n" );
document.write( "\n" );
document.write( "please teach me through this. 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 #52309 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=52309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This equation models the decay of a radioactive element. As time goes on the element decays and we want to know how much of the original amount <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D ALIGN=MIDDLE  ALT=\"A%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > we should collect to have 40 grams after 3 days of decay. Since t represents the number of days, let t=3 and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D ALIGN=MIDDLE  ALT=\"A%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40=A%5Bo%5De%5E%28-0.18%283%29%29 ALIGN=MIDDLE  ALT=\"40=A%5Bo%5De%5E%28-0.18%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Set the decay model equal to 40 (after 3 days it decays to 40 grams. If you plug in t=3, you get 40)Note: e is a constant<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fe%5E%28-0.54%29=%28A%5Bo%5D%2Across%28e%5E%28-0.54%29%29%29%2F%28cross%28e%5E%28-0.54%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-0.54%29 ALIGN=MIDDLE  ALT=\"e%5E%28-0.54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=40%2Fe%5E%28-0.54%29 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=40%2Fe%5E%28-0.54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=40%2F0.582748 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=40%2F0.582748\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=40%2F0.582748 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=40%2F0.582748\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=68.64030%0D%0A ALIGN=MIDDLE  ALT=\"A%5Bo%5D=68.64030%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >Approximately<BR>\n" );
document.write( "So about 68.6 grams should remain after 3 days\r<BR>\n" );
document.write( "\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%2868.64030%29e%5E%28-0.18%28t%29%29 ALIGN=MIDDLE  ALT=\"A=%2868.64030%29e%5E%28-0.18%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If I let t=3 I should get A=40 (40 grams left over)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%2868.64030%29e%5E%28-0.18%283%29%29 ALIGN=MIDDLE  ALT=\"A=%2868.64030%29e%5E%28-0.18%283%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=A=%2868.64030%29%280.582748%29 ALIGN=MIDDLE  ALT=\"A=%2868.64030%29%280.582748%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=39.9999975444%0D%0A ALIGN=MIDDLE  ALT=\"A=39.9999975444%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >Which is really close to 40, so this answer works\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );