document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129640>Question 1129640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. \r<BR>\n" );
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document.write( "Write an exponential equation f(t) representing this situation. (Let f be the amount of radioactive substance in grams and t be the time in minutes.) \r<BR>\n" );
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document.write( "To the nearest minute, what is the half-life of this substance?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746253 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=746253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A scientist begins with 250 grams of a radioactive substance.<BR>\n" );
document.write( " After 250 minutes, the sample has decayed to 32 grams. <BR>\n" );
document.write( "Write an exponential equation f(t) representing this situation. (Let f be the amount of radioactive substance in grams and t be the time in minutes.) <BR>\n" );
document.write( "To the nearest minute, what is the half-life of this substance?<BR>\n" );
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document.write( "A = Ao*2^(-t/h) is the radioactive decay formula, where<BR>\n" );
document.write( "A = remaining amt after t time (32 gr)<BR>\n" );
document.write( "Ao = initial amt (250 gr)<BR>\n" );
document.write( "t = time (250 minutes)<BR>\n" );
document.write( "h = half-life of substance<BR>\n" );
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document.write( "250*2^(-250/h) = 32<BR>\n" );
document.write( "divide both sides by 250<BR>\n" );
document.write( "2^(-250/h) = .128<BR>\n" );
document.write( "ln(2^(250/h)) = ln(.128)<BR>\n" );
document.write( "log equiv of exponent<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-250%2Ft ALIGN=MIDDLE  ALT=\"-250%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >*ln(2) = ln(.128)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-250%2Ft ALIGN=MIDDLE  ALT=\"-250%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.128%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%28.128%29%2Fln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using your calc<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-250%2Ft ALIGN=MIDDLE  ALT=\"-250%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -2.9658<BR>\n" );
document.write( "-2.9658t = -250<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-250%29%2F%28-2.9658%29 ALIGN=MIDDLE  ALT=\"%28-250%29%2F%28-2.9658%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 84.3 ~ 84 minutes is the half life of the substance </SPAN>\n" );
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