document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134649>Question 134649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a radioactive substance is decaying at a rate of 34% per year. Initially you have 500 grams of the substance.\r<BR>\n" );
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document.write( "Explain why the amount of the radioactive substance is an exponential function<BR>\n" );
document.write( "Explain why the yearly decay factor is a =0.66.<BR>\n" );
document.write( "Write a formula for the amount of the radioactive substance.<BR>\n" );
document.write( "How many grams will be left after two years?<BR>\n" );
document.write( "After how many years will there be only 11 grams left?<BR>\n" );
document.write( "What is the monthly decay factor (to three decimal places)?<BR>\n" );
document.write( "What is the monthly percentage decay rate?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98508 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=98508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose a radioactive substance is decaying at a rate of 34% per year. Initially you have 500 grams of the substance.<BR>\n" );
document.write( "A(t) = A(0)*0.66^t <BR>\n" );
document.write( "Explain why the amount of the radioactive substance is an exponential function<BR>\n" );
document.write( "Because each year there is 66% of what there was last year.<BR>\n" );
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document.write( "Explain why the yearly decay factor is a =0.66.<BR>\n" );
document.write( "66% of last years amount  is how much of the material remains after one year.<BR>\n" );
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document.write( "Write a formula for the amount of the radioactive substance.<BR>\n" );
document.write( "A(t)= 500*0.66^t<BR>\n" );
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document.write( "How many grams will be left after two years?<BR>\n" );
document.write( "A(2) = 500*0.66^2 = 217.80 grams<BR>\n" );
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document.write( "After how many years will there be only 11 grams left?<BR>\n" );
document.write( "11 = 500*0.66^t<BR>\n" );
document.write( "tlog(.66) = log(11/500)<BR>\n" );
document.write( "t = [log(11/500)]/[log0.66]<BR>\n" );
document.write( "t = 9.1855 years<BR>\n" );
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document.write( "What is the monthly decay factor (to three decimal places)?<BR>\n" );
document.write( "The yearly decay rate is 34%; The monthly decay rate is 0.34^(1/12) = 0.914<BR>\n" );
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document.write( "What is the monthly percentage decay rate?<BR>\n" );
document.write( "A(0) = 500<BR>\n" );
document.write( "A(1/12) = 500*0.66^(1/12)= 482.9832<BR>\n" );
document.write( "A(1/12)/A(0) = 482.9832/500 = 0.9660 (amount left after one month)<BR>\n" );
document.write( "Monthly percentage decay rate = 1-0.9660 = 0.034 = 3.4%<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "Qua <BR>\n" );
document.write( " </SPAN>\n" );
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