Question

How many days have passed if 4.80 mg of calcium-47 decayed to 1.2 mg of calcium-47?

Answer 1

(1) 36 days is 8 half-life periods,
so 24mg becomes 24mg times (1/2)^8 = 24 mg/256 = 0.094 mg

(2) 9.6/1.2 = 8, which means three half-life periods went by.
At the end of 4.5 days, there were 4.8 mg
At the end of 9.0 days, there were 2.4 mg
At the end of 13.5 days, there were 1.2 mg

(3) The activity is proportional to the amount of radioactive material remaining,
so after two half-life periods, the activity should be 1/4 of what it originally was.
So the initial activity was probably 12.0 Ci