Final answer:
To calculate the remaining amount of a radioactive substance after a given time period, we use the half-life concept. For a substance with a 3-month half-life, after 21 months, we determine the number of half-lives that have passed and apply the formula, yielding approximately 0.15625 lbs remaining from the original 20 lbs.
Step-by-step explanation:
To calculate the amount of a radioactive substance left after a certain period, given its half-life, we can use the concept of half-life which is the time it takes for half of the original amount of a radioactive substance to decay. In this case, the half-life of the substance is 3 months. To find out how much of the 20 lbs of the substance would remain after 21 months, we need to determine how many half-lives have passed in that time frame.
Calculation:
- First, we divide the total time elapsed (21 months) by the half-life of the substance (3 months) to get the number of half-lives that have passed:
21 months / 3 months per half-life = 7 half-lives. - Next, we apply the half-life decay formula:
Final amount = Initial amount × (½)^number of half-lives
Final amount = 20 lbs × (½)^7 - Calculating this we get:
Final amount = 20 lbs × 0.0078125 (which is (½)^7) - Final amount = 0.15625 lbs
Therefore, after 21 months, there would be approximately 0.15625 lbs of the radioactive substance left in the treasure chest.