Question 242817
I am guessing that your original substance starts at 400 and you are looking to find when A(t)=200.
In this case, you would have {{{1/2=e^.045t}}}
To solve this, you would take the natural log (ln e) of both sides.
{{{ln(1/2)=ln(e^.045t)}}}
the rules of logarithms says that log (a/b)=log a - log b
so, ln 1 -ln 2 =.045t
use your calculator to finish this and you get t=-15.40 years.  I think your formula may have a negative missing or something.  I don't deal a lot with half life, but this is how you would do it and D is the right answer.

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