document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=843241>Question 843241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the associated exponential decay or growth model.<BR>\n" );
document.write( "Q = 1,800 when t = 0; half-life = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508029 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39625)</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=508029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve this generally for k:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=Qe%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"A=Qe%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
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document.write( "Let t=5, A=(1/2)Q, , and find the formula this way for k.\r<BR>\n" );
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document.write( "Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1800e%5E%28-k%2At%29 ALIGN=MIDDLE  ALT=\"A=1800e%5E%28-k%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the value you found for k.\r<BR>\n" );
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document.write( "Best if you follow that and do it.<BR>\n" );
document.write( "I did not show you the specific steps.  Do you need them?\r<BR>\n" );
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document.write( "SOLUTION WITH NEARLY ALL STEPS SHOWN--------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28A=Qe%5E%28-kt%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28A=Qe%5E%28-kt%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------Basic Model for Decay<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29=ln%28Q%29%2Bln%28e%5E%28-kt%29%29 ALIGN=MIDDLE  ALT=\"ln%28A%29=ln%28Q%29%2Bln%28e%5E%28-kt%29%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%28A%29-ln%28Q%29=-kt%2A1 ALIGN=MIDDLE  ALT=\"ln%28A%29-ln%28Q%29=-kt%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28k=%28ln%28Q%29-ln%28A%29%29%2Ft%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=%28ln%28Q%29-ln%28A%29%29%2Ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The specific example has initial half life of 5 years, t=5 with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=Q%2F2 ALIGN=MIDDLE  ALT=\"A=Q%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, enough for finding the value of k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%28Q%2FA%29%2Ft ALIGN=MIDDLE  ALT=\"k=ln%28Q%2FA%29%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%28Q%2F%28Q%2F2%29%29%2F5 ALIGN=MIDDLE  ALT=\"k=ln%28Q%2F%28Q%2F2%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28k=ln%282%29%2F5%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=ln%282%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But as a decimal number, this can be stated <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=0.1386%29 ALIGN=MIDDLE  ALT=\"highlight%28k=0.1386%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The specific model equation based on given Q=1800 and the found value for k, becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28A=1800%2Ae%5E%28-0.1386%2At%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28A=1800%2Ae%5E%28-0.1386%2At%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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