document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126105>Question 126105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The formula for describing the amount of radioactive Plutonium-35 is A=Ao(1/2)(^t/4370),where A is the remaining amount of Plutonium-35 and t is the time given in years.<BR>\n" );
document.write( "a) When will the remaining Plutonium-35 be 1/8 of the original amount?<BR>\n" );
document.write( "b) When will the remaining Plutonium-35 be 1/sqrt2 of the original amount?<BR>\n" );
document.write( "c) When will the remaining Plutonium-35 be 1/sqrt32 of the original amount?<BR>\n" );
document.write( " I am not sure if I have typed the Formala A=Ao(1/2)^t/4370 correctly. I don't know if I should say A= Abase0(1/2)(^t/4370).Can someone clarify this for me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92429 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=92429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for describing the amount of radioactive Plutonium-35 is<BR>\n" );
document.write( "A(t) = Ao(1/2)^(t/4370),where A is the remaining amount of Plutonium-35 and t is the time given in years<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "This formula means:<BR>\n" );
document.write( "A(t) is the amount of the plutonium at time \"t\"<BR>\n" );
document.write( "Ao is the amount of plutonium you start with<BR>\n" );
document.write( "(1/2) is the decrease rate<BR>\n" );
document.write( "t/4370 means the half-life is 4370 yearsevery 4370 years you multiply by (1/2)<BR>\n" );
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document.write( "I'll do part \"a\" and leave the others to you.<BR>\n" );
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document.write( "a) When will the remaining Plutonium-35 be 1/8 of the original amount?<BR>\n" );
document.write( "(1/8)Ao = Ao(1/2)^(t/4370)<BR>\n" );
document.write( "(1/8) = (1/2)^(t/4370)<BR>\n" );
document.write( "Take the log of both sides to get:<BR>\n" );
document.write( "log(1/8) = (t/4370)log (1/2)<BR>\n" );
document.write( "t/4370 = [log(1/8)/log(1/2)] = 3<BR>\n" );
document.write( "t = 13110 yrs<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "b) When will the remaining Plutonium-35 be 1/sqrt2 of the original amount?<BR>\n" );
document.write( "c) When will the remaining Plutonium-35 be 1/sqrt32 of the original amount?<BR>\n" );
document.write( " I am not sure if I have typed the Formala A=Ao(1/2)^t/4370 correctly. I don't know if I should say A= Abase0(1/2)(^t/4370).Can someone clarify this for me? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );