If the half-life is 80,000 years, then 240,000 years would be equivalent to three half-lives. In other words, the initial amount of the radioactive calcium-41 would have been reduced in half three times over. Mathematically, this can expressed as
calcium-41 remaining = initial mass of calcium-41 × (0.5)³.
Since we are given the initial mass of calcium-41, the amount of calcium-41 remaining after 240,000 years would be:
60 μg × (0.5)³ = 7.5 μg, or 7.5 micrograms.
