Consider the differential equation for the population p

Chapter 1, Problem 7E

(choose chapter or problem)

Consider the differential equation

$\frac{d p}{d t}=p(p-1)(2-p)$

for the population p (in thousands) of a certain species at time t.

(a) Sketch the direction field by using either a computer software package or the method of isoclines.

(b) If the initial population is 4000 [ that is, $p(0)=4$], what can you say about the limiting population $\lim _{t \rightarrow+\infty} p(t)$?

(d) If $p(0)=0.8$, what is $\lim _{t \rightarrow+\infty} p(t)$?

(e) Can a population of 900 ever increase to 1100?

Equation Transcription:

$\frac{dp}{dt}=p(p-1)(2-p)$

$p(0)=4$

$li{m}_{t\rightarrow{}+\infty{}}p(t)$

$p(0)=1.7$

$li{m}_{t\rightarrow{}+\infty{}}p(t)$

$p(0)=0.8$

$li{m}_{t\rightarrow{}+\infty{}}p(t)$

Text Transcription:

dp over dt=p(p-1)(2-p)

p(0)=4

lim_t+infinity p(t)

p(0)=1.7

lim_t+infinity p(t)

p(0)=0.8

lim_t+infinity p(t)

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