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 \(\boxed{73}\).