Show that in case of a first order reaction, the time required for `99.9%` of the reaction to take place is about `10` times that the required for half the reaction.

Explanation

To show that in the case of a first-order reaction, the time required for `99.9%` of the reaction to take place is about `10` times that required for half the reaction, we can follow these steps:

### Step 1: Understand the first-order reaction kinetics
For a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant. The integrated rate law for a first-order reaction is given by:

\[ t = \frac{2.303}{k} \log \left( \frac{[A_0]}{[A]} \right) \]
...