A species of animal is discovered on an island. Suppose that the population size $P(t)$ of the species can be modeled by measured in years.
\[
P(t)=\frac{400}{1+2 e^{-0.18 t}}
\]
Find the initial population size of the species and the population size after 8 years. Round your answers to the nearest whole number as necessary.

Step 1 ：A species of animal is discovered on an island. Suppose that the population size $P(t)$ of the species can be modeled by the equation \[P(t)=\frac{400}{1+2 e^{-0.18 t}}\] where $t$ is the time measured in years.

Step 2 ：The initial population size can be found by substituting $t=0$ into the equation.

Step 3 ：By substituting $t=0$ into the equation, we get \[P(0)=\frac{400}{1+2 e^{-0.18 \cdot 0}}\] which simplifies to \[P(0)=\frac{400}{1+2}\] and further simplifies to \[P(0)=133\] when rounded to the nearest whole number.

Step 4 ：The population size after 8 years can be found by substitifying $t=8$ into the equation.

Step 5 ：By substituting $t=8$ into the equation, we get \[P(8)=\frac{400}{1+2 e^{-0.18 \cdot 8}}\] which simplifies to \[P(8)=271\] when rounded to the nearest whole number.

Step 6 ：Final Answer: The initial population size of the species is \(\boxed{133}\) and the population size after 8 years is \(\boxed{271}\).