physics

a radioactive sample has a decay rate R of 518 decay/min at time t=7 min and 156 decay/ min at time t=17 min. calculate the decay constant and the initial decay rate?

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  1. a = Ai e^-kt
    da/dt = -kAi e^-kt

    518 = -k e^-7k

    156 = -k e^-17k

    518/156 = e^-7k / e^-17k = e^10k

    ln 3.32 = 10 k

    1.2 = 10 k
    k = .12

    I guess you can take it from there

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  2. assuming an exponential function with initial value f(t) = a,

    a*e^-kt, we have

    a*e^-7k = 518
    a*e^-17k = 156
    so, dividing, e^10k = 156/518
    k = -0.12

    f(t) = ae^-.12t
    a*e^-.84 = 518
    a = 1200

    f(t) = 1200 e^-0.12t

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