Exponential and Logarithmic Functions Finding the rate or time in a word problem on continuous exponential. Español The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of $1.8 \%$ 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. Dominic Español

Step 1 ：The problem is asking for the time it takes for a population of bacteria to double given a continuous growth rate of 1.8% per hour. This is a classic problem of exponential growth, which can be modeled by the formula \(P = P0 * e^{rt}\), where \(P\) is the final amount, \(P0\) is the initial amount, \(r\) is the growth rate, and \(t\) is the time.

Step 2 ：In this case, we know that \(P/P0 = 2\) (since the population doubles), and \(r = 1.8/100\) (converting the percentage to a decimal). We need to solve for \(t\).

Step 3 ：We can rearrange the formula to get \(t = \ln(P/P0) / r\). Since \(P/P0 = 2\), we can substitute this into the formula to get \(t = \ln(2) / r\).

Step 4 ：We can then plug in the given growth rate to find the time it takes for the population to double.

Step 5 ：Final Answer: It takes approximately \(\boxed{38.51}\) hours for the size of the sample to double.