The activity of a radioactive sample falls from `600 s^(-1) to 500 s^(-1) in 40 minutes. Calculate its half-life.

Explanation

To solve the problem of calculating the half-life of a radioactive sample whose activity falls from \(600 \, s^{-1}\) to \(500 \, s^{-1}\) in 40 minutes, we can follow these steps:

### Step 1: Understand the relationship between activity and decay constant
The activity \(A\) of a radioactive sample at time \(t\) can be expressed using the formula:
\[ A = A_0 e^{-\lambda t} \]
where:
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