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Math Help - Exponential Decay

  1. #1
    Member realintegerz's Avatar
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    Exponential Decay

    A substance undergoes radioactive decay. If you start with 3 grams, after 4 seconds you will have 1 gram left.

    a) How long will it take to have 2 grams left?
    b) How much will you have after 6 seconds?
    c) What is the half-life of the substance?

    I have asked about these problems on this site multiple times and I am still very confused on how to do these decay and growth problems , any help would be appreciated
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  2. #2
    Member
    Joined
    Jan 2009
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    Amount left = initial amount * e^(rate * time)

    1 = 3 * e^ (rate * 4)

    Let's solve for the rate:

    1/3 = e^(4r)
    ln(1/3) = 4r
    (1/4)ln(1/3) = r

    a) How long will it take to have 2 grams left?
    Solve for time in this equation:

    2 = 3 e^(rt) // we solved for r above, plug it in and isolate t


    b) How much will you have after 6 seconds?
    Solve for y:

    y = 3 e^(6r) // again we found r above


    c) What is the half-life of the substance?
    Solve for t:

    (3/2) = 3 e^(rt) // once more, we already know r.



    These styles of problem have 4 variables: final amount, initial amount, rate, and time. Arrange a problem that plugs in 3 things, and find the 4th.
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