The radioisotope `""_(15)^(32)P` is used in biochemical studies. A sample containing this isotope has an activity 1000 times the detectable limit. How long could an experiment be run with the sample before the radioactivity could no longer be detected ? Half-life of `""_(15)^(32)P` is 14.2 days

Explanation

To solve the problem, we need to determine how long the experiment can be run with the sample of the radioisotope \( _{15}^{32}P \) before the radioactivity falls below the detectable limit. We know the half-life of the isotope is 14.2 days and that the initial activity is 1000 times the detectable limit.

### Step-by-Step Solution:

1. **Understand the Concept of Half-Life**:
The half-life of a radioactive substance is the time required for half of the radioactive atoms in a sample to decay. For \( _{15}^{32}P \), the half-life is given as 14.2 days.

2. **Determine the Initial Activity**:
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