document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998642>Question 998642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show step by step. Thanks\r<BR>\n" );
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document.write( "An unknown radioactive element decays into non-radioactive substances. In 980  days the radioactivity of a sample decreases by 52  percent. \r<BR>\n" );
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document.write( " (a) What is the half-life of the element? <BR>\n" );
document.write( " half-life:       (days) \r<BR>\n" );
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document.write( " (b) How long will it take for a sample of 100  mg to decay to 77  mg? <BR>\n" );
document.write( " time needed </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616413 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=616413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> General model  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=pe%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"y=pe%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you have starter information so that you can find the value for k.  Also half-life.\r<BR>\n" );
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document.write( "The 52% decrease after 980 days,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fp=e%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"y%2Fp=e%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%2Fp%29=-kt ALIGN=MIDDLE  ALT=\"ln%28y%2Fp%29=-kt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28p%2Fy%29=kt ALIGN=MIDDLE  ALT=\"ln%28p%2Fy%29=kt\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------------------(and this step you will use again).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=%281%2Ft%29ln%28p%2Fy%29%29 ALIGN=MIDDLE  ALT=\"highlight%28k=%281%2Ft%29ln%28p%2Fy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Information given in description is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28t=980%2Adays%2Cp=100%2Cy=48%29 ALIGN=MIDDLE  ALT=\"system%28t=980%2Adays%2Cp=100%2Cy=48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and this \"48\" is because that is what remains as percent after 52% decayed.\r<BR>\n" );
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document.write( "You should be able to do the rest of the questions and steps.\r<BR>\n" );
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document.write( "Still wanted more steps to the solutions---\r<BR>\n" );
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document.write( "(a) Half-Life\r<BR>\n" );
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document.write( "Return to this part: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28p%2Fy%29=kt ALIGN=MIDDLE  ALT=\"ln%28p%2Fy%29=kt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What was k?  Substitute the given values in the main part of the description!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%28100%2F48%29%2F980 ALIGN=MIDDLE  ALT=\"k=ln%28100%2F48%29%2F980\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=7.489%2A10%5E%28-4%29%29 ALIGN=MIDDLE  ALT=\"highlight%28k=7.489%2A10%5E%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The model for decay is now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=pe%5E%28-0.0007489%2At%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=pe%5E%28-0.0007489%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "The step to find any time t,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=ln%28p%2Fy%29%2Fk ALIGN=MIDDLE  ALT=\"t=ln%28p%2Fy%29%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You know the needed values for finding half-life with this formula, so substitute THEM.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=ln%281%2F%281%2F2%29%29%2F0.0007489 ALIGN=MIDDLE  ALT=\"t=ln%281%2F%281%2F2%29%29%2F0.0007489\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=925%2Adays%29 ALIGN=MIDDLE  ALT=\"highlight%28t=925%2Adays%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----the half-life.\r<BR>\n" );
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document.write( "(b)  How long to decay from 100 mg to 77 mg ?<BR>\n" );
document.write( "You have the formula and model to use. </SPAN>\n" );
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