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6-77.

The half-life of an isotope is 1000 years. A 50-gram sample of the isotope is sealed in a box. Homework Help ✎

  1. How much is left after 10,000 years?

    Half-life means time in which half of the original 50 grams will remain.

    y = abn

    a is the initial value,
    b is the multiplier (0.5 since we are working with a half-life),
    n is the number of thousands of years, and
    y is the amount of the isotope that remains (in grams).

    The equation is y = 50(0.5)x. Substitute 10 for x.

    Use the equation below, where x is the number of years.

  2. How long will it take to reduce to 1% of the original amount?

    Use the equation from the help for part (a).
    In this case, y = 1% of 50 and you are solving for x.

    ≈ 6600 years

  3. How long will it take until all of the original sample of the isotope is gone? Support your answer.