The number of bacteria $P(t)$ in a certain population increases according to the following function, where time $t$ is measured in hours. \[ P(t)=2300 e^{0.18 t} \] Find the number of bacteria in the population after 3 hours and after 8 hours. Round your answers to the nearest whole number as necessary.

Step 1 ：The problem is asking for the number of bacteria after 3 hours and 8 hours. This can be found by substituting \(t=3\) and \(t=8\) into the given function \(P(t)=2300 e^{0.18 t}\) and calculating the result.

Step 2 ：Substitute \(t=3\) into the function to get \(P(3)=2300 e^{0.18 \times 3}\).

Step 3 ：Calculate the result to get \(P(3) \approx 3947\).

Step 4 ：Substitute \(t=8\) into the function to get \(P(8)=2300 e^{0.18 \times 8}\).

Step 5 ：Calculate the result to get \(P(8) \approx 9708\).

Step 6 ：Final Answer: The number of bacteria in the population after 3 hours is approximately \(\boxed{3947}\) and after 8 hours is approximately \(\boxed{9708}\).