Final answer:
The half-life of a radioactive substance can be calculated using a decay formula where the initial amount, final amount, and elapsed time are known. The decay formula is rearranged and solved for the half-life using logarithms.
Step-by-step explanation:
To determine the half-life of a radioactive substance based on its decay over a set period, we use the formula N_t = N_0 (1/2)^(t/T), where N_t is the remaining amount of the substance at time t, N_0 is the original amount, and T is the half-life. In this case, we started with 40 mg of a substance and ended with 29.5 mg after one year.
We assume the decay process follows first-order kinetics (a common assumption for nuclear decay), so we need to solve for T when N_t = 29.5 mg and N_0 = 40 mg. This involves taking the logarithm of both sides of the equation and rearranging to isolate T.