[tex]P(t)[/tex] gives the population after [tex]t[/tex] years. The initial population is the one observed before the passage of any time, or [tex]P(0)[/tex].
[tex]P(0)=\dfrac{1000}{1+7e^{-0.42\cdot0}}=\dfrac{1000}{1+7}=125[/tex]
The population after 8 years is given by [tex]P(8)[/tex].
[tex]P(8)=\dfrac{1000}{1+7e^{-0.42\cdot8}}\approx804[/tex]
