document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=331902>Question 331902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help:<BR>\n" );
document.write( "Suppose you have 500 grams of a radioactive element whose half life is 72 years.\r<BR>\n" );
document.write( "\n" );
document.write( "a) Find the function for the quantity, Q, left in t years.\r<BR>\n" );
document.write( "\n" );
document.write( "b) Find to the nearest tenth of a year when there will be 100 grams left. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #237930 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=237930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose you have 500 grams of a radioactive element whose half life is 72 years.<BR>\n" );
document.write( "a) Find the function for the quantity, Q, left in t years.<BR>\n" );
document.write( "b) Find to the nearest tenth of a year when there will be 100 grams left.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Exponential decay/growth formula:<BR>\n" );
document.write( "N = Noe^(rt)<BR>\n" );
document.write( "where<BR>\n" );
document.write( "N is amount after t time<BR>\n" );
document.write( "No is the initial amount<BR>\n" );
document.write( "r is rate of decay<BR>\n" );
document.write( "t is years<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Find r from \"500 grams of a radioactive element whose half life is 72 years\":<BR>\n" );
document.write( "N = Noe^(rt)<BR>\n" );
document.write( ".5(500) = 500e^(r*72)<BR>\n" );
document.write( ".5 = e^(r*72)<BR>\n" );
document.write( "ln(.5) = r*72<BR>\n" );
document.write( "ln(.5)/72 = r<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Replacing r with the above in:<BR>\n" );
document.write( "N = Noe^(rt)<BR>\n" );
document.write( "To get:<BR>\n" );
document.write( "N = 500e^(tln(.5)/72)<BR>\n" );
document.write( "which ANSWERS part a.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Part b:<BR>\n" );
document.write( "b) Find to the nearest tenth of a year when there will be 100 grams left.<BR>\n" );
document.write( "Starting with:<BR>\n" );
document.write( "N = 500e^(tln(.5)/72)<BR>\n" );
document.write( "Replace N with 100 and solve for t<BR>\n" );
document.write( "100 = 500e^(tln(.5)/72)<BR>\n" );
document.write( ".2 = e^(tln(.5)/72)<BR>\n" );
document.write( "ln(.2) = tln(.5)/72<BR>\n" );
document.write( "72ln(.2) = tln(.5)<BR>\n" );
document.write( "72ln(.2)/ln(.5) = t<BR>\n" );
document.write( "167.2 years = t\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );