The mass of a radioactive substance decreases exponentially at a rate of 3% each day.(i) Find the overall percentage decrease at the end of 10 days

To solve this problem, we need to understand that the decrease is not linear, but exponential. This means that each day, the substance decreases by 3% of its current mass, not its original mass.

Here are the steps to solve this problem:

1. First, we need to express the daily decrease as a decimal. Since the substance decreases by 3% each day, we can express this as 0.03.

2. Next, we need to calculate the daily multiplier. Since the substance is decreasing, we subtract the daily decrease from 1. This gives us 1 - 0.03 = 0.97. This means that each day, the substance retains 97% of its mass from the previous day.

3. To find the overall decrease after 10 days, we raise the daily multiplier to the power of 10. This gives us 0.97^10 = 0.7374 (rounded to four decimal places). This means that after 10 days, the substance retains about 73.74% of its original mass.

4. Finally, to find the overall percentage decrease, we subtract the remaining percentage from 100%. This gives us 100% - 73.74% = 26.26%.

So, the overall percentage decrease at the end of 10 days is approximately 26.26%.