document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=849667>Question 849667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use a graph to approxiamate the age of rock that has 70% of its original K40. 50%=1.3 billion yrs, 25%=2.6 billion.. thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511705 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=511705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  use a graph to approximate the age of rock that has 70% of its original K40. 50%=1.3 billion yrs, 25%=2.6 billion..<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Assign the given data as:<BR>\n" );
document.write( "x1 = 50; y1 = 1.3<BR>\n" );
document.write( "x2 = 25; y2 = 2.6<BR>\n" );
document.write( "Find the slope using m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.6-1.3%29%2F%2825-50%29 ALIGN=MIDDLE  ALT=\"%282.6-1.3%29%2F%2825-50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.3%2F25 ALIGN=MIDDLE  ALT=\"-1.3%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the equation using the point/slope form; y - y1 = m(x-x1)<BR>\n" );
document.write( "y - 1.3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.3%2F25 ALIGN=MIDDLE  ALT=\"-1.3%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 50)<BR>\n" );
document.write( "y - 1.3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.3%2F25 ALIGN=MIDDLE  ALT=\"-1.3%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2.6<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.3%2F25 ALIGN=MIDDLE  ALT=\"-1.3%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2.6 + 1.3<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.3%2F25 ALIGN=MIDDLE  ALT=\"-1.3%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 3.9<BR>\n" );
document.write( "Graph this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+105%2C+-2%2C+5%2C+%28-1.3%2F25%29x+%2B+3.9%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+105%2C+-2%2C+5%2C+%28-1.3%2F25%29x+%2B+3.9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "putting this graph in my calc, At 70% the age is only .26 billion yrs<BR>\n" );
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document.write( "As I walked away from this problem to do some menial labor, it occurred <BR>\n" );
document.write( "to me that his may a radioactive decay proble. They gave us the half-life<BR>\n" );
document.write( "when they said 50% at 1.3 million yrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "solve it that way with 70% remaining using the decay formula using logs<BR>\n" );
document.write( "A = Ao*2(-h/t),<BR>\n" );
document.write( "where<BR>\n" );
document.write( "A = amt remaining after t time, we will say this is .7<BR>\n" );
document.write( "Ao = initial amt (t=0), we will call this 1<BR>\n" );
document.write( "t = time of decay (billions of yrs here)<BR>\n" );
document.write( "h = half-life of substance 1.3 billion years<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1*2^(-t/1.3) = .7<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F1.3 ALIGN=MIDDLE  ALT=\"-t%2F1.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >log(2) = log(.7)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F1.3 ALIGN=MIDDLE  ALT=\"-t%2F1.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28.7%29%2Flog%282%29 ALIGN=MIDDLE  ALT=\"log%28.7%29%2Flog%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F1.3 ALIGN=MIDDLE  ALT=\"-t%2F1.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.51457<BR>\n" );
document.write( "t = -1.3 *-.51457<BR>\n" );
document.write( "t = +.669 billion yrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graphing this, Green line represents 70%, x = billions of yrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1%2C+4%2C+-1%2C+1%2C+2%5E%28-x%2F1.3%29%2C+.7%29 ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-1%2C+4%2C+-1%2C+1%2C+2%5E%28-x%2F1.3%29%2C+.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Would appreciate if you would let me know which is right here. CK<BR>\n" );
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