document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129572>Question 1129572</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. 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? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746142 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=746142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 32/250=0.128<BR>\n" );
document.write( "A=Ao*2(-t/h)<BR>\n" );
document.write( "32=250*2(-t/h)<BR>\n" );
document.write( "0.128=2*(-250/h)<BR>\n" );
document.write( "ln(0.128)=-250/h * ln2<BR>\n" );
document.write( "divide both sides by ln2 and multiply by h<BR>\n" );
document.write( "-2.9658h=-250<BR>\n" );
document.write( "h=84.29 min or 84 min\r<BR>\n" );
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document.write( "0.128 is almost decayed 3 half lives, and 3 half lives would be 252 minutes, which is reasonable. </SPAN>\n" );
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