The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of $8.2 \%$ per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).
Note: This is a continuous exponential decay model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.
days

Step 1 ：The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 8.2% per day. We are asked to find the half-life of this substance, that is, the time it takes for one-half the original amount in a given sample of this substance to decay.

Step 2 ：The half-life of a substance under exponential decay can be calculated using the formula: \(T = \frac{\ln(2)}{\lambda}\), where \(T\) is the half-life and \(\lambda\) is the decay rate.

Step 3 ：In this case, the decay rate is given as 8.2% per day, which is equivalent to 0.082 in decimal form.

Step 4 ：Substituting the given values into the formula, we get \(T = \frac{\ln(2)}{0.082}\).

Step 5 ：Solving this equation gives us \(T \approx 8.45\) days.

Step 6 ：Final Answer: The half-life of the substance is approximately \(\boxed{8.45}\) days.