Answer:
Option A)
[tex]\displaystyle\lim_{t\to\infty}~p(t) = k[/tex]
Step-by-step explanation:
We are given the following on the question:
[tex]p(t) =\displaystyle\frac{4000}{4+e^{-0.02t}}[/tex]
where p(t) is the population of a colony.
For steady state solution we evaluate:
[tex]\displaystyle\lim_{t\to\infty}~p(t)\\\\= \lim_{x\to\infty} \frac{4000}{4+e^{-0.02t}}\\\\=\frac{4000}{4+e^{-\infty}}\\\\=\frac{4000}{4}\\\\= 1000[/tex]
Thus, the steady state solution is a constant, k = 1000.
Thus, the correct answer is
Option A)
[tex]\displaystyle\lim_{t\to\infty}~p(t) = k[/tex]
