A piece of wood form the ruins of an ancient building was found to have a `C^(14)` activity of 12 disintegrations per minute per gram of its carbon content. The `C^(14)` activity of the living wood is 16 disintegrations/minute/gram. How long ago did the trees, from which the wooden sample came, die? Given half-life of `C^(14)` is 5760 years.

Explanation

To determine how long ago the trees from which the wooden sample came died, we can use the information provided about the activity of Carbon-14 (`C^(14)`) and its half-life. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Current activity of the wood sample (`A_t`): 12 disintegrations/minute/gram
- Initial activity of living wood (`A_0`): 16 disintegrations/minute/gram
- Half-life of `C^(14)` (`t_half`): 5760 years

### Step 2: Calculate the decay constant (λ)
...