Final answer:
The half-life of the radioactive substance is approximately 0.699 years.
Step-by-step explanation:
The half-life of a radioactive substance is the time it takes for half of the sample to decay.
In this case, the substance decayed to 96.5% of its original amount after a year. This means that 100% - 96.5% = 3.5% of the substance decayed in a year.
Since the substance decayed by half in a year, we can calculate the half-life using the following equation: 0.5^t = 0.965, where t is the number of half-lives.
Taking the logarithm of both sides, we get:
t * log(0.5) = log(0.965)
t = log(0.965) / log(0.5) ≈ 0.699 years