In a given radioactive sample, it is observed that after 415.8 days, 12.5% of the initial sample remains undecayed. Calculate the mean life and decay constant of this sample.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
We know that after 415.8 days, 12.5% of the initial sample remains undecayed. This means that:
- Initial amount of the sample, \( N_0 \)
- Remaining amount after 415.8 days, \( N = 0.125 N_0 \)

### Step 2: Relate the remaining amount to the decay formula
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