Pre-calculus

Initially 600 milligrams of a radioactive substance was present. After 7 hours the mass had decreased by 3%. Construct an exponential model
A(t) = A0ekt for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24 hours.

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asked by Kim
  1. so
    600(.97) = 600 e^(7k)
    .97 = e^(7k)
    ln .97 = 7k lne
    7k = ln .97
    k = ln .97/7 = -.004351315

    amount = 600 e^-.0043511315t
    so when t = 24
    amount = 600 e^-.104431..
    = .900836(600) ----> 90.08% remain
    = 540.50 mg

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    posted by Reiny

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