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Math Help - half life solving initial quantity

  1. #1
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    half life solving initial quantity

    half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

    I need to solve for the initial quantity with the info given, thx for the help
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by theman View Post
    half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

    I need to solve for the initial quantity with the info given, thx for the help
    we use the equation I(t) = I_0e^{rt}

    where r is the rate of decay, I(t) is the amount at time t, I_0 is the intial amount (what we are searching for).

    now, \mbox{half-life} = \frac {\ln 2}r

    you know the half-life, so you can find r.

    once you have r. plug in I(t) = 1.5, t = 1000, and r = whatever. and solve for I_0
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    thanks, but i still dun know how to solve for the rate of the decay...
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  4. #4
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    Quote Originally Posted by Jhevon View Post
    now, \mbox{half-life} = \frac {\ln 2}r

    you know the half-life, so you can find r.
    Quote Originally Posted by theman View Post
    thanks, but i still dun know how to solve for the rate of the decay...
    You can't solve that equation for r??

    -Dan
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  5. #5
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    lol, sorry, im kinda stupid, but i just solved it thanks!
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  6. #6
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    um, sorry, but one more thing. With the same info and the initial quantity i got was 2.3 g. How would u solve it for 10,000 years.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by theman View Post
    um, sorry, but one more thing. With the same info and the initial quantity i got was 2.3 g. How would u solve it for 10,000 years.
    I = I_0 e^{rt}

    You have I_0 and r. Just plug in t = 10000 years.

    -Dan
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  8. #8
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    Quote Originally Posted by theman View Post
    half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

    I need to solve for the initial quantity with the info given, thx for the help
    double posts .
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