A species of fish was added to a lake. The population size P (t) of this species can be modeled by the following function, where t is the number of years from the time the species were added to the lake.Find the population size of the species after 4 years and the population size after 8 yearsRound your answers to the nearest whole number as necessary.

Explanation:[tex]\begin{gathered} \text{The given function:} \\ P(t)\text{ = }\frac{1200}{1+8e^{-0.15t}} \\ \\ We\text{ n}eed\text{ to find the }P(t)\text{ when t = 4 years and t = 8 years} \end{gathered}[/tex][tex]\begin{gathered} \text{when t = 4 years} \\ \text{substitute 4 for t in the given function} \\ P(t)\text{ = }\frac{1200}{1+8e^{-0.15(4)}} \\ P(t)\text{ = }\frac{1200}{1+4.3905}\text{= }\frac{1200}{5.3905} \\ P(t)\text{ = }222.61 \\ \\ To\text{ the nearest whole number, population size is 223 fishes} \end{gathered}[/tex][tex]\begin{gathered} \text{when t = 8 years} \\ P(t)\text{ = }\frac{1200}{1+8e^{-0.15(8)}} \\ P(t)\text{ =}\frac{1200}{1+2.4096}\text{ = }\frac{1200}{3.4096} \\ P(t)\text{ = }351.95 \\ \\ To\text{ the nearest whole number, population size is 352 fishes} \end{gathered}[/tex]