Problem: 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 was added to the lake. $$P(t)=\frac{2500}{1+4e^{-0.1t}}$$ Find the initial population size of the species and the population size after $8$ years.
My work:
after 8 years:
\begin{align}P(8)&= \frac{2500}{1+4e^{-0.1(8)}}\\ &=\frac{2500e^{0.8}}{e^{0.8} +4}\\ &=894 \end{align}
initial:
$$P(0)= \frac{2500}{1+4e^{-0.1(0)}}$$
This is where I am stuck..
What is the next step that I need?
$\endgroup$ 31 Answer
$\begingroup$$$P(0) = \frac{2500}{1+4e^{-(0.1)0}}=\frac{2500}{1+4e^{0}}=\frac{2500}{1+4}=500$$
$\endgroup$
