Ответ

Transcribing and analyzing

The problem states that a radioactive substance reduces its mass by half every week. After some time, the mass is reduced to 1 kg. The task is then to determine how many kilograms were initially placed in the container.

The experiment lasted for 6 weeks, and a second trial started with 7.8 kg less than the initial mass. The goal is to calculate the initial mass based on this halving behavior. I’ll need to reverse the process and calculate carefully.

Solving for initial mass

For the first batch of substance, it decays from an initial mass, M, to 1 kg over a time $t_1$ weeks. The second batch starts with $M - 7.8$ kg and decays to 1 kg over time $t_2$, with the total time being 6 weeks. Using the halving equation $M \times (1/2)^{t_1} = 1$ and $(M - 7.8) \times (1/2)^{t_2} = 1$, I derive the equation $M^2 - 7.8M - 64 = 0$. Solving this gives M = 12.8 kg.

Thought for 1m 5s