document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270807>Question 270807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following table shows the amount of polonium in milligrams remaining after x days from an original sample of 2 milligrams.<BR>\n" );
document.write( "x(days)           0  100     200      300<BR>\n" );
document.write( "y milligrams  2  1.22  0.743  0.453\r<BR>\n" );
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document.write( "a. is the half life pf te polonium less than 200 days?<BR>\n" );
document.write( "b. give a general formula thatr can be used to approximate the amount A of polonium after x days.<BR>\n" );
document.write( "c. what is the half-life of the polonium? GRaph A(x) and show th epoint that would show the half-life for x=2 milligrams. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198336 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=198336\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The following table shows the amount of polonium in milligrams remaining after x days from an original sample of 2 milligrams.<BR>\n" );
document.write( "x(days) 0 100 200 300<BR>\n" );
document.write( "y milligrams 2 1.22 0.743 0.453<BR>\n" );
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document.write( "a. is the half life of the polonium less than 200 days?<BR>\n" );
document.write( "Find the half life (h) using values for 100 days and resulting amt of 1.22 mg<BR>\n" );
document.write( "2*(2^(-100/h)) = 1.22<BR>\n" );
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document.write( "2^(-100/h) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.22%2F2 ALIGN=MIDDLE  ALT=\"1.22%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "2^(-100/h) = .61<BR>\n" );
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document.write( "log(2^(-100/h)) = log(.61)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100%2Fh ALIGN=MIDDLE  ALT=\"-100%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >log(2) = log(.61)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100%2Fh ALIGN=MIDDLE  ALT=\"-100%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28.61%29%2Flog%282%29 ALIGN=MIDDLE  ALT=\"log%28.61%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=-100%2Fh ALIGN=MIDDLE  ALT=\"-100%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.713<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F.713 ALIGN=MIDDLE  ALT=\"100%2F.713\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h ~ 140 days is the half life<BR>\n" );
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document.write( "b. give a general formula that can be used to approximate the amount A of polonium after x days.<BR>\n" );
document.write( "A = 2*2^(-x/140)<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "c. what is the half-life of the polonium?<BR>\n" );
document.write( "we found it to be 140 days in (a)<BR>\n" );
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document.write( " GRaph A(x) and show th epoint that would show the half-life for x=2 milligrams.<BR>\n" );
document.write( "Graph the equation y = 2*2^(-x/140)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-50%2C+325%2C+-1%2C+3%2C+2%2A2%5E%28-x%2F140%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-50%2C+325%2C+-1%2C+3%2C+2%2A2%5E%28-x%2F140%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see that at 140 days there is about 1 mg of the substance<BR>\n" );
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