A container is filled with a radioactive substance for which the half- life is 2 days. A week later, when the container is opened, it contains 5 g of the substance. Approximately how many grams of the substance were initially placed in the container?

[c] For this substance 7 days correspond to 3.5 half- lives. Over 3 half- lifes the sample reduces to 123=18 of its initial mass. After 4 half- lifes, the sample has only 124=116of its initial mass. Hence, after 3.5 half- lives the sample must contain somewhere between 1/8 and 1/16 of its initial mass. Hence 5 g is somewhere between 1/8 and 1/16 of the initial mass. So, the initial mass is somewhere between 8×5=40g and 16×5=80g.