# question about decay

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• Aug 16th 2009, 06:56 AM
andres
question about decay
I would like to know which one is the right formula to calculate the decay if the book is asking to find the remaining radioactive salt after 75 years, knowing that the decay rate is 2% and we had 100 kg at the beginning. The book's result is 22kg after 75 years, so which one of these 2 formulas should be the right one?

$\displaystyle x=100(e^(-0.02*75))$

or

$\displaystyle x=100(0.98^75)$

Ps. with both of them, I get pretty close the book's answer

Thanks
• Aug 16th 2009, 08:06 AM
skeeter
Quote:

Originally Posted by andres
I would like to know which one is the right formula to calculate the decay if the book is asking to find the remaining radioactive salt after 75 years, knowing that the decay rate is 2% and we had 100 kg at the beginning. The book's result is 22kg after 75 years, so which one of these 2 formulas should be the right one?

$\displaystyle x=100(e^(-0.02*75))$

or

$\displaystyle x=100(0.98^75)$

Ps. with both of them, I get pretty close the book's answer

Thanks

radioactive decay is considered to have a continuous rate, and the decay rate can be modeled by the DE

$\displaystyle \frac{dy}{dt} = -.02y$

which leads to the solution equation $\displaystyle y = 100e^{-.02t}$

I interpret the equation $\displaystyle y = 100(0.98)^t$ to model a decay rate of 2% per year.