The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of $9.8 \%$ 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
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Step 1 ：The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 9.8% per day. We are asked to find the half-life of this substance, which 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 9.8% per day. We need to convert this percentage to a decimal before we can use it in the formula. So, \(\lambda = \frac{9.8}{100} = 0.098\).

Step 4 ：We can now substitute these values into the formula to find the half-life of the substance. \(T = \frac{\ln(2)}{0.098}\)

Step 5 ：Calculating the above expression, we find that \(T = 7.072930413876993\)

Step 6 ：Rounding to the nearest hundredth, we find that the half-life of the substance is approximately \(\boxed{7.07}\) days.