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calculus

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A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.)
(a) What is the half-life of the substance?
(b) How long would it take the sample to decay to 65% of its original amount?

  • calculus - ,

    general equation

    amount = starting (1/2)^(t/k) , where t is the time and k is the half-life period

    a)
    .945 = 1(.5)^1/k
    ln .945 = (1/k)ln.5
    1/k = ln.945/ln.5
    k = ln.5/ln.945 = 12.25 years

    b)
    .65 = (.5)^t/12.25
    t/12.25 = ln.65/ln.5 = .621488..
    t = 7.61 years

  • calculus - ,

    A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents time in years and y
    represents the amount of the isotope left then the equation for the situation is y= y0e-0.0002t. In how many years will there be 93% of the isotope left?

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