half life problem

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• Jul 11th 2007, 03:22 PM
davecs77
half life problem
I have this problem:
The half-life of radium is 1690 years. How much will be left of 32 grams of radium after 6760 years?
I know to use the formula:
y = Ce^(kx) Where C is the original amount, y is the future amount, k is rate, and x is time. I am having some trouble figuring out what pieces go where. I am thinking the 1690 years is the x, but I'm not so sure of the rest. Also..this is off topic, but is it fine that I am asking a lot (maybe too many in some opinions) questions? I have been strugling with calc 2 since I started it monday. The class is Mon-Fri, 2 hours each day. This is a good way for me to learn..by practicing and finding out what I am doing right/wrong to improve my skills. Thanks everyone.
• Jul 11th 2007, 03:38 PM
galactus
The decay constant k is $\displaystyle \frac{-1}{T}ln(2)=\frac{-1}{1690}ln(2)\approx{-0.00041014626...}$

At t=0 there is 32 grams, so that $\displaystyle y(6760)=32e^{-0.00041014626(6760)}= 2 \;\ grams$
• Jul 11th 2007, 03:51 PM
davecs77
Quote:

Originally Posted by galactus
The decay constant k is $\displaystyle \frac{-1}{T}ln(2)=\frac{-1}{1690}ln(2)\approx{-0.00041014626...}$

At t=0 there is 32 grams, so that $\displaystyle y(6760)=32e^{-0.00041014626(6760)}= 2 \;\ grams$

How did you find the decay constant?
• Jul 11th 2007, 04:25 PM
galactus
By the formula I gave you.

$\displaystyle k=\frac{-1}{T}ln(2)$.

That comes from halving time being given by $\displaystyle T=\frac{-1}{k}ln(2)$