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The half-life of a radioactive substance is 1500 years.
\n" ); document.write( "a) What does the model look like if we use an exponential decay model (base e)?
\n" ); document.write( "
\n" ); document.write( "Explain what each part of the model represents.
\n" ); document.write( "A = resulting amt after t time
\n" ); document.write( "Ao = initial amt of the substance (t=0)
\n" ); document.write( "k = decay rate of the substance (derived from the half-life)
\n" ); document.write( "t = time of decay
\n" ); document.write( ":
\n" ); document.write( "b) If we start with 100 mg of the substance, how much of it will still be radioactive in 2000 years.
\n" ); document.write( " find k, the decay rate, we know we have half of it left after 1500 yrs
\n" ); document.write( "k =
\n" ); document.write( "k = -.0004621
\n" ); document.write( "now we can solve for remaining substance after 2000 years
\n" ); document.write( "A =
\n" ); document.write( "A = 39.68 mg
\n" ); document.write( " Does your answer make sense? yes we know it is less than half which is 50
\n" ); document.write( ":
\n" ); document.write( "c) If we start with 100 mg of the substance, how much of it will still be radioactive in 10,000 years.
\n" ); document.write( "A =
\n" ); document.write( "A = .9843 mg
\n" ); document.write( "Does your answer make sense?, yes, very little left after 10000 years
\n" ); document.write( ":
\n" ); document.write( "d) Will the 100mg ever completely dissipate (ie to 0 mg radioactive)? If so, when? Clearly explain why or why not.
\n" ); document.write( "Effectively, it will become so tiny, it can be considered 0, but theoretically it never reaches 0 as the time goes on to infinity. For example after 100000 yrs is will be about