Math

A radioactive substance decays according to the formula
Q(t) = Q0e−kt
where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay constant.
(a) Find the half-life of the substance in terms of k.

(b) Suppose a radioactive substance decays according to the formula
Q(t) = 36e−0.0001074t
How long will it take for the substance to decay to half the original amount? (Round your answer to the nearest whole number.)

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  1. .5 = e^-k T
    ln .5 = - k T

    T = -.693/-k = .693/k

    b)
    T = .693 / .0001074 = 6454 years

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    2. 👎
  2. A radioactive substance decays according to the formula
    Q(t) = Q0e−kt
    where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay constant.
    (a) Find the half-life of the substance in terms of k.

    (b) Suppose a radioactive substance decays according to the formula
    Q(t) = 36e−0.0001238t
    How long will it take for the substance to decay to half the original amount? (Round your answer to the nearest whole number.)

    1. 👍
    2. 👎

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