In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the of the substance was 1500 grams and mass was decreasing by 10per day. Determine the mass of the radioactive sample at the beginning of the 10th day of the experiment. Round to the nearest tenth if necessary).
To determine the mass of the radioactive sample at the beginning of the 10th day of the experiment, we need to calculate the remaining mass after 9 days of decay.
Given:
Initial mass (day 0) = 1500 grams
Decay rate = 10% per day
First, calculate the mass remaining after 9 days:
Mass remaining after 9 days = Initial mass * (1 - decay rate)^number of days
Mass remaining after 9 days = 1500 * (1 - 0.10)^9
Mass remaining after 9 days ≈ 1500 * (0.9)^9
Mass remaining after 9 days ≈ 1500 * 0.387420489
Mass remaining after 9 days ≈ 581.1307335 grams
Therefore, the mass of the radioactive sample at the beginning of the 10th day of the experiment is approximately 581.1 grams.