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Pre Calc

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The half-Life of radioactive earthium is 2651 years. Find how many years it will take 100 grams of earthium to decay to 10 grams.


I know the equation is A=Ae^(-rt)

I tried working it out but I think I am doing it wrong.
I did 10=100e^(-r*2651)

Can anyone help? Thanks a lot

  • Pre Calc - ,

    If you want to use the e^kt function then you can find k the following way.

    .5 = 1(e^2651k)
    ln .5 = 2651k
    k = ln.5/2651 = -.000261466

    so we need:
    10 = 100(e^ -.000261466t)
    .1 = e^ -.000261466t
    -.000261466t = ln .1
    t = ln .1 / .000261466
    t = 8806 years

    or

    Since you know you are dealing with half-life, we could use the equation

    10 = 100 (.5)^(t/2651)
    t/2651 = l .1 / ln .5
    t = 8806

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