SOLUTION: can someone please help me with this problem: A certain radioactive isotope decays at a rate of 0.25% annually. Determine the half - life of this isotope, to the nearest year.

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Question 163533: can someone please help me with this problem:
A certain radioactive isotope decays at a rate of 0.25% annually. Determine the half - life of this isotope, to the nearest year.
a. 120 years
b. 277 years
c. 200 years
d. 3 years
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The isotope follows this power law as a function of time,
N%28t%29=N%5B0%5D%28.9975%29%5Et
where t is measured in years and N%5B0%5D is the initial amount of the isotope.
Half life is when N%28t%29=%281%2F2%29N%5B0%5D,
%281%2F2%29N%5B0%5D=N%5B0%5D%280.9975%29%5Et
%280.5%29=%280.9975%29%5Et
t=log%280.9975%2C0.5%29
t=276.9
.
.
.
Looks like b) 277 years is the closest answer.