The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of $5 \%$ per hour. How many hours does it take for the size of the sample to double? Note: This is a continuous exponential growth model. Do not round any intermediate computations, and round your answer to the nearest hundredth.

Step 1 ：We are given a continuous exponential growth model, which is represented by the formula \(N(t) = N_0 * e^{rt}\), where \(N(t)\) is the final amount, \(N_0\) is the initial amount, \(r\) is the growth rate, and \(t\) is the time.

Step 2 ：In this problem, we want to find the time it takes for the population to double. This means that \(N(t) = 2 * N_0\).

Step 3 ：We can set up the equation \(2 = e^{0.05t}\) and solve for \(t\).

Step 4 ：By solving the equation, we find that \(t = 13.862943611198904\).

Step 5 ：Rounding to the nearest hundredth, we find that it takes approximately \(\boxed{13.86}\) hours for the size of the sample to double.