Question

In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 1400 grams and mass was decreasing by 8% per day. Determine the mass of the radioactive sample at the beginning of the 17th day of the experiment. Round to the nearest tenth (if necessary).

Answer 1

The mass of the radioactive sample at the beginning of the 17th day of the experiment is approximately 368.8 grams.

Explanation:

Since the mass of the substance is decreasing by 8% per day, this means that the remaining mass after each day is 92% of the mass from the previous day.

To find the mass of the radioactive sample at the beginning of the 17th day of the experiment, we can use the formula:

mass = initial mass * (0.92)^n

where n is the number of days that have passed since the beginning of the experiment.

On the 17th day of the experiment, n = 16 (since we're counting the first day as day 0). So, we have:

mass = 1400 * (0.92)^16

Using a calculator, we can find that this simplifies to:

mass ≈ 368.8 grams

Therefore, the mass of the radioactive sample at the beginning of the 17th day of the experiment is approximately 368.8 grams.