Find the half-life period of a radioactive material if its activity drops of `(1/16)^(th)` of its initial value in 40 years.

Explanation

To find the half-life period of a radioactive material given that its activity drops to \( \frac{1}{16} \) of its initial value in 40 years, we can follow these steps:

### Step 1: Understand the Problem
We know that the initial activity \( R_0 \) drops to \( \frac{R_0}{16} \) in 40 years.

### Step 2: Write the Activity Formula
The activity \( R \) at time \( t \) is given by the formula:
\[
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