Equal masses of two samples of charcoal `A and B` are burnt separately and the resulting carbon dioxide are collected in two vessels. The radioactivity of `^14 C` is measured for both the gas samples. The gas from the charcoal A gives `2100 counts` per week and the gas from the charcoal A gives 2100 counts per week and the gas from the charcoal `B` gives `1400` counts per week. Find the age difference between the two samples. Half-life of `^14 C = 5730 y`.

Explanation

To find the age difference between the two charcoal samples A and B based on their radioactivity measurements, we can follow these steps:

### Step 1: Understand the relationship between activity and time
The activity of a radioactive sample decreases over time according to the equation:
\[ A = A_0 e^{-\lambda t} \]
where:
- \( A \) is the activity at time \( t \),
- \( A_0 \) is the initial activity,
...