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 300 grams
and mass was decreasing by 6% per day. Determine the mass of the radioactive
sample at the beginning of the 16th day of the experiment. Round to the nearest tenth
(if necessary).

Answer 1

To solve this problem, we can use the formula for exponential decay:

m = m0(1 - r)^t

where:

m0 = initial mass (300 grams)

r = decay rate (6% per day, or 0.06)

t = time in days

We want to find the mass at the beginning of the 16th day, so t = 15:

m = 300(1 - 0.06)^15

m ≈ 107.4

Therefore, the mass of the radioactive sample at the beginning of the 16th day of the experiment is approximately 107.4 grams.