Question

For the following system, determine if a steady state exists and give the steady state value. The population of a colony of squirrels is given by p(t) = 4000/4 + e^-0.02t. For which of the following situations does there exist a steady state? A. lim_t rightarrow infinity f(t) = k, where k is a finite number. B. lim_t rightarrow infinity f(t) = plusminus infinity C. lim_t rightarrow infinity f(t) does not exist and is neither infinity nor -infinity.

Answer 1

Answer:

Option A)

$\displaystyle\lim_{t\to\infty}~p(t) = k$

Step-by-step explanation:

We are given the following on the question:

$p(t) =\displaystyle\frac{4000}{4+e^{-0.02t}}$

where p(t) is the population of a colony.

For steady state solution we evaluate:

$\displaystyle\lim_{t\to\infty}~p(t)\\\\= \lim_{x\to\infty} \frac{4000}{4+e^{-0.02t}}\\\\=\frac{4000}{4+e^{-\infty}}\\\\=\frac{4000}{4}\\\\= 1000$

Thus, the steady state solution is a constant, k = 1000.

Thus, the correct answer is

Option A)

$\displaystyle\lim_{t\to\infty}~p(t) = k$