document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139499>Question 1139499</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 28 grams. Write an exponential equation <BR>\n" );
document.write( "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" );
document.write( "\n" );
document.write( "To the nearest minute, what is the half-life of this substance? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #759963 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=759963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let n be the number of half-lives.  Then, since the substance decays by a factor of 0.5 every half-life, the amount of the original 250g remaining after n half-lives is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+250%280.5%29%5En ALIGN=MIDDLE  ALT=\"f%28t%29+=+250%280.5%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If the half-life is k minutes, then the number of half-lives in t minutes is t/k.  Then the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+250%280.5%29%5E%28t%2Fk%29 ALIGN=MIDDLE  ALT=\"f%28t%29+=+250%280.5%29%5E%28t%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The half-life k can be determined from the given information that the original 250g decays to 28g in 250 minutes:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28+=+250%280.5%29%5E%28250%2Fk%29 ALIGN=MIDDLE  ALT=\"28+=+250%280.5%29%5E%28250%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.112+=+0.5%5E%28250%2Fk%29 ALIGN=MIDDLE  ALT=\"0.112+=+0.5%5E%28250%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%280.112%29%29+=+%28250%2Fk%29%2Alog%28%280.5%29%29 ALIGN=MIDDLE  ALT=\"log%28%280.112%29%29+=+%28250%2Fk%29%2Alog%28%280.5%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=k+=+250%2Alog%28%280.5%29%29%2Flog%28%280.112%29%29+=+79.153 ALIGN=MIDDLE  ALT=\"k+=+250%2Alog%28%280.5%29%29%2Flog%28%280.112%29%29+=+79.153\"   DISABLED_style= \"max-width:90%; height:auto;\" > to 3 decimal places.<br><BR>\n" );
document.write( "ANSWER: to the nearest minute, the half-life of the substance is 79 minutes. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );