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calculus

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Question: "Plutonium isotope Pu-239 has a half-life of 24,100 years. Suppose that 10 grams of Pu-239 was released in the Chernobyl nuclear accident. How long will it take for the 10 grams to decay to 1 gram?"

I know that I am suppose to use
y= ye^kt , to get the equation and then plug in the info. to get the time, but I'm not sure how to start, please help! Thanks!

  • calculus -

    y = a e^(kt) where a is the initial amount
    so y = 10(e^(kt))
    when t = 24100, y = 5 ---> you should have 1/2 of the original 10 g left.

    0.5 = e^(24100k)
    24100k = ln(0.5)
    k = ln(.5)/24100
    so y = 10(e^(t)(ln.5/24100))
    so you want y to be 1

    1 = 10 (e^(t)(ln.5/24100))
    0.1 = (e^(t)(ln.5/24100))

    (t)(ln.5/24100)) = ln .1
    t = 80059

    so about 80,000 years !!!!

  • calculus -

    Ohhh, I get it!! Thanks so much, you helped me a lot! :)

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