document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198803>Question 1198803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Radon is a naturally occurring radioactive gas which can collect in poorly ventilated structures. Radon gas is formed by the decomposition of radium-226 which has a half life of 1622 years. The half-life of radon is 3.82 days. Suppose a house basement contained 38 grams of radon gas when a family moved in. If the source of radium producing the radon gas is removed so that the radon gas eventually decays, how long will it take until there is only 6.8 grams of radon gas present? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832698 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Radon is a naturally occurring radioactive gas which can collect in poorly ventilated structures. Radon gas is formed by the decomposition of radium-226 which has a half life of 1622 years. The half-life of radon is 3.82 days. Suppose a house basement contained 38 grams of radon gas when a family moved in. If the source of radium producing the radon gas is removed so that the radon gas eventually decays, how long will it take until there is only 6.8 grams of radon gas present?<BR>\n" );
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;\">Neither a dissertation nor a novel needs to be written, as one person did, in order to solve this.\r\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29-life ALIGN=MIDDLE  ALT=\"%281%2F2%29-life\"   DISABLED_style= \"max-width:90%; height:auto;\" > is given as \"a\" time periods, then k, the DECAY CONSTANT = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2C+ln%281%2F2%29%2Fa%2C+or%2C+ln%28.5%29%2Fa%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C3%2C+ln%281%2F2%29%2Fa%2C+or%2C+ln%28.5%29%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r\n" );
document.write( "So, we get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C6%2C+k%2C+%22=%22%2C+ln%281%2F2%29%2F3.82%2C+%22=%22%2C+-+.1815%2C+%22%28approximately%29%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( " \r\n" );
document.write( "                    Continuous GROWTH/DECAY formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2C+A%2C+%22=%22%2C+A%5Bo%5De%5E%28kt%29%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C3%2C+A%2C+%22=%22%2C+A%5Bo%5De%5E%28kt%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "                                                   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2C+6.8%2C+%22=%22%2C+38e%5E%28-+.1815t%29%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C3%2C+6.8%2C+%22=%22%2C+38e%5E%28-+.1815t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- Substituting 6.8 for A, 38 for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D ALIGN=MIDDLE  ALT=\"A%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and - .1815 for k\r\n" );
document.write( "                                                   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C3%2C+6.8%2F38%2C+%22=%22%2C+e%5E%28-+.1815t%29%2C+3.4%2F19%2C+%22=%22%2C+e%5E%28-+.1815t%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "                                              <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2C+-+.1815t%2C+%22=%22%2C+ln+%283.4%2F19%29%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C3%2C+-+.1815t%2C+%22=%22%2C+ln+%283.4%2F19%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ Converting to LOGARITHMIC (natural) form\r\n" );
document.write( "Time it'll take the radon to reduce to 6.8 grams, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28matrix%281%2C6%2C+t%2C+%22=%22%2C+ln+%283.4%2F19%29%2F%28-+.1815%29%2C+%22=%22%2C+highlight%289.4802%29%2C+days%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></PRE> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );