document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130378>Question 1130378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A laboratory has a 750g sample of uranium. This substance has a half life of 20 years. \r<BR>\n" );
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document.write( "a) Write an equation to represent the mass of the substance after x half lives.<BR>\n" );
document.write( "b) how many half-lives will have elapsed in 120 years ?<BR>\n" );
document.write( "c) How much of the sample is left after 120 years?\r<BR>\n" );
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document.write( "Thank you<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747035 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=747035\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "Part A\r<BR>\n" );
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document.write( "Start off with 750 grams of the material. After 1 half-life, you have 750*(1/2) = 375 grams. After 2 half-lives, you have 750*(1/2)*(1/2) = 187.5 grams. This pattern continues. The number of half-lives determines how many copies of (1/2) you will multiply.\r<BR>\n" );
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document.write( "If there were 5 copies of (1/2), then this refers to 5 half-lives. We can write it as (1/2)*(1/2)*(1/2)*(1/2)*(1/2) or we can use exponentials as a shortcut and say (1/2)^5\r<BR>\n" );
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document.write( "If there are x half-lives that occur, then we multiply by (1/2)^x\r<BR>\n" );
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document.write( "Therefore, <font color=red>the equation is y = 750*(1/2)^x</font> where x is the number of half-lives and y is the amount of material remaining.\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "\"A half life of 20 years\" means that every 20 year mark has the amount of uranium cut in half. Refer to part A.\r<BR>\n" );
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document.write( "Divide 120 over 20 to get 120/20 = 6.\r<BR>\n" );
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document.write( "There are <font color=red>6 half-lives</font> in 120 years.\r<BR>\n" );
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document.write( "Part C\r<BR>\n" );
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document.write( "From part B, we found that 120 years is 6 half-lives for this material, so x = 6.\r<BR>\n" );
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document.write( "Plug x = 6 into the equation found in part A. Use the order of operations PEMDAS to simplify.\r<BR>\n" );
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document.write( "y = 750*(1/2)^x\r<BR>\n" );
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document.write( "y = 750*(1/2)^6 .... replace x with 6\r<BR>\n" );
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document.write( "y = 750*(0.5)^6\r<BR>\n" );
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document.write( "y = 750*0.015625\r<BR>\n" );
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document.write( "y = 11.71875\r<BR>\n" );
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document.write( "There is <font color=red>11.71875 grams</font> of uranium left after 120 years.<BR>\n" );
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