document.write( "Question 632073: Hospitals use radioactive substance iodine-131 in their researches.A hospital purchased 40 grams of the substance.Eight days later,when a doctor wanted to use some of the iodine-131,he found out that only 20 grams remained.Predict the amount remaining two weeks after purchase. \n" ); document.write( "
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Hospitals use radioactive substance iodine-131 in their researches.A hospital purchased 40 grams of the substance.Eight days later,when a doctor wanted to use some of the iodine-131,he found out that only 20 grams remained.Predict the amount remaining two weeks after purchase.
\n" ); document.write( "A = Pe^(kt)
\n" ); document.write( "determine exponential decay constant k:
\n" ); document.write( "20 = 40e^(k*8)
\n" ); document.write( ".5 = e^(k*8)
\n" ); document.write( "ln(.5) = k*8
\n" ); document.write( "ln(.5)/8 = k
\n" ); document.write( ".
\n" ); document.write( "Our equation is now:
\n" ); document.write( "A = 40e^(t*ln(.5)/8)
\n" ); document.write( ".
\n" ); document.write( "Now we can answer:Predict the amount remaining two weeks after purchase.
\n" ); document.write( "two weeks is equivalent to 14 days:
\n" ); document.write( "thus t =14
\n" ); document.write( "A = 40e^(t*ln(.5)/8)
\n" ); document.write( "A = 40e^(14*ln(.5)/8)
\n" ); document.write( "A = 40e^(-1.213)
\n" ); document.write( "A = 11.89 grams\r
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