If a material has a half-life of 2 years, how much of a 1 kg sample remains after 8 years?

To determine how much of a 1 kg sample remains after 8 years given a half-life of 2 years, we can apply the concept of half-lives directly. The half-life is the time it takes for half of the material to decay.

1. Start with an initial mass of 1 kg.

2. After the first half-life of 2 years, half of the material remains: 1 kg / 2 = 0.5 kg.

3. After the second half-life (4 years), half of 0.5 kg remains: 0.5 kg / 2 = 0.25 kg.

4. After the third half-life (6 years), half of 0.25 kg remains: 0.25 kg / 2 = 0.125 kg.

5. After the fourth half-life (8 years), half of 0.125 kg remains: 0.125 kg / 2 = 0.0625 kg.

Therefore, after 8 years, the remaining amount of the material is 0.0625 kg, which aligns with the understanding that each completed half-life reduces the mass of the original sample by half. The closest representation of this value provided in the