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" );
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document.write( "I find the formula for radioactive decay easier to understand if we write it in terms of number of half-lives, instead of in terms of numbers of days (or hours, or years, or milliseconds).<br><BR>\n" );
document.write( "The amount of a radioactive sample remaining after n half-lives is the original amount, 250g, multiplied by 1/2 to the power n.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28n%29+=+250%28.5%29%5En ALIGN=MIDDLE  ALT=\"f%28n%29+=+250%28.5%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We are given that after 250 minutes the amount remaining is 32g.  Use that to find the number of half-lives there are in 250 minutes.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+=+250%28.5%29%5En ALIGN=MIDDLE  ALT=\"32+=+250%28.5%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.128+=+.5%5En ALIGN=MIDDLE  ALT=\"0.128+=+.5%5En\"   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%28.128%29%29+=+n%2Alog%28%28.5%29%29 ALIGN=MIDDLE  ALT=\"log%28%28.128%29%29+=+n%2Alog%28%28.5%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=n+=+log%28%28.128%29%29%2Flog%28%28.5%29%29 ALIGN=MIDDLE  ALT=\"n+=+log%28%28.128%29%29%2Flog%28%28.5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.9658 to 4 decimal places<br><BR>\n" );
document.write( "The half life is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250%2F2.9658 ALIGN=MIDDLE  ALT=\"250%2F2.9658\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 84.2947 minutes to 4 decimal places<br><BR>\n" );
document.write( "The formula for the remaining amount as a function of the number of minutes t (with n = t/84.2947) is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+250%28.5%29%5E%28t%2F84.2947%29 ALIGN=MIDDLE  ALT=\"f%28t%29+=+250%28.5%29%5E%28t%2F84.2947%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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