A sample of bacteria is growing at an hourly rate of $10 \%$ according to the continuous exponential growth function. Th sample began with 6 bacteria.

How many bacteria will be in the sample after 25 hours? Round your answer down to the nearest whole number.

Provide your answer below:

Step 1 ：Given that the initial amount of bacteria, \(N_0 = 6\), the growth rate, \(r = 10\% = 0.1\), and the time, \(t = 25\) hours.

Step 2 ：We can use the continuous exponential growth function, which is given 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 3 ：Substitute the given values into the formula to find the number of bacteria after 25 hours: \(N_t = 6 * e^{0.1*25}\).

Step 4 ：Calculate the value of \(N_t\) to get the final number of bacteria.

Step 5 ：Round down the final number to the nearest whole number.

Step 6 ：Final Answer: The number of bacteria in the sample after 25 hours will be \(\boxed{73}\).