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Math Help - half life problem

  1. #1
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    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.
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  2. #2
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    The decay constant k is \frac{-1}{T}ln(2)=\frac{-1}{1690}ln(2)\approx{-0.00041014626...}

    At t=0 there is 32 grams, so that y(6760)=32e^{-0.00041014626(6760)}= 2 \;\ grams
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  3. #3
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    Quote Originally Posted by galactus View Post
    The decay constant k is \frac{-1}{T}ln(2)=\frac{-1}{1690}ln(2)\approx{-0.00041014626...}

    At t=0 there is 32 grams, so that y(6760)=32e^{-0.00041014626(6760)}= 2 \;\ grams
    How did you find the decay constant?
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  4. #4
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    By the formula I gave you.

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

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