document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187575>Question 1187575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A radioactive form of uranium has a half life of 2.5x 10^5 years. a) Find the remaining mass of 1 g sample after t years<BR>\n" );
document.write( "b) Determine the remaining mass of this sample after 5000 years. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818592 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A radioactive form of uranium has a half life of 2.5x 10^5 years. <BR>\n" );
document.write( "a) Find the remaining mass of 1 g sample after t years<BR>\n" );
document.write( "b) Determine the remaining mass of this sample after 5000 years.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In his post, @Theo makes tons of absolutely unnecessary work, &nbsp;unnecessary calculations \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and unnecessary explanations, &nbsp;making simple problem hopelessly confused and showing you &nbsp;WRONG &nbsp;WAY &nbsp;doing job.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Had some student come to his teacher and present a solution like @Theo does in his post,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the teacher would only shrug shoulders &nbsp;(out of curtesy).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came with two goals: &nbsp;&nbsp;1) &nbsp;&nbsp;to make the solution in a regular/normal simple manner, &nbsp;and \r<BR>\n" );
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document.write( "                       &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2) &nbsp;&nbsp;to make the solution in a way &nbsp;<U>HOW &nbsp;TO &nbsp;&nbsp;it should be done and presented</U>.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Since the half life is given, we write the decay equation using the \" base 2 \" exponent function\r\n" );
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document.write( "    m(t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%280%29%2A%281%2F2%29%5E%28t%2F250000%29 ALIGN=MIDDLE  ALT=\"m%280%29%2A%281%2F2%29%5E%28t%2F250000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "for a current mass m(t),  where m(0) is the initial mass of the sample.\r\n" );
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document.write( "Now we simply substitute the given values into the formula and calculate\r\n" );
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document.write( "(a)  1 gram sample after t years  m(t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E%28t%2F250000%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E%28t%2F250000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  grams.\r\n" );
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document.write( "(b)  the remaining mass of this sample after 5000 years is  m(5000) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E%285000%2F250000%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E%285000%2F250000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E%281%2F50%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E%281%2F50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E0.02 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E0.02\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.9862327.    <U>ANSWER</U>\r\n" );
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document.write( "That is all.  &nbsp;&nbsp;&nbsp;&nbsp;The problem is just solved and completed.\r<BR>\n" );
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document.write( "What you need to know to solve such problems, &nbsp;is &nbsp;THIS:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- there are different forms of exponential decay equations: &nbsp;1) &nbsp;ekt-form; &nbsp;2) &nbsp;\" base 2 \" &nbsp;form; &nbsp;and &nbsp;3) &nbsp;an arbitrary &nbsp;\" base &nbsp;b \" form.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- each form is good for its own purposes and problems;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- if the problem's data is given in half-life terms, &nbsp;always use &nbsp;\" base 2 \" &nbsp;form and make all calculations in this form;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;do not change this form in the course of the solution, &nbsp;until the problem asks you to change the base explicitly.\r<BR>\n" );
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document.write( "On radioactive decay, &nbsp;see the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/logarithm/Radioactive-decay-problems.lesson>Radioactive decay problems</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "You will find many similar &nbsp;(and different) &nbsp;solved problems there.\r<BR>\n" );
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document.write( "Use this lesson as your handbook, &nbsp;textbook, &nbsp;guide, &nbsp;tutorials, and &nbsp;(free of charge) &nbsp;home teacher.\r<BR>\n" );
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document.write( "Learn the subject from there once and for all.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in &nbsp;ALGEBRA-I &nbsp;in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lesson is the part of this online textbook under the topic \"<U>Logarithms</U>\".\r<BR>\n" );
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document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-I<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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