SOLUTION: How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t)=400e^0.045t, where t is the time in yea

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Question 242817: How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t)=400e^0.045t, where t is the time in years? Round to the nearest hunderedth year.
The answeres could be
A: 18.00 years
B: 133.14 years
C: 148.55 years
D: 15.40 years
I think the answer is 15.40 years. Please let me know for sure.
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F2=e%5E.045t
To solve this, you would take the natural log (ln e) of both sides.
ln%281%2F2%29=ln%28e%5E.045t%29
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.
For further questions, I can be reached at justin.sheppard.tech@hotmail.com