document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277974>Question 277974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP!!<BR>\n" );
document.write( "The radioactive isotope thorium 234 has a half-life of approximately 578 hours.<BR>\n" );
document.write( "a) If a sample has an initial mass of 64 mg, a function that models the mass in mg after t hours is a(t)= _____________ ?<BR>\n" );
document.write( "b) The amount remaining after 75 hours will be about __________ mg. <BR>\n" );
document.write( "c) The initial mass will decay to 12 mg after ________ hours.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202333 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=202333\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The redioactive isotope thorium 234 has a half-life of approximately 578 hours.<BR>\n" );
document.write( "A(t) = Ao*(1/2)^(t/578)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "a) If a sample has an initial mass of 64 mg, a function that models the mass in mg after t hours is a(t)= 64*(1/2)^(t/578)<BR>\n" );
document.write( "---------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "b) The amount remaining after 75 hours will be about __________ mg.<BR>\n" );
document.write( "A(75) = 64*(1/2)^(75/578)<BR>\n" );
document.write( "A(75) = 64*0.914<BR>\n" );
document.write( "A(75) = 58.5 mg<BR>\n" );
document.write( "-------------------------------- <BR>\n" );
document.write( "c) The initial mass will decay to 12 mg after ________ hours. <BR>\n" );
document.write( "solve 12 = 64*(1/2)^(t/578)<BR>\n" );
document.write( "(1/2)^(t/578) = 0.1875<BR>\n" );
document.write( "Take the natural log of both sides to get:<BR>\n" );
document.write( "(t/578)ln(1/2) = ln(0.1875)<BR>\n" );
document.write( "t/578 = 2.4150<BR>\n" );
document.write( "t = 1395.89 hrs.<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );