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 \(\lim _{t \rightarrow+\infty} p(t)\)?
(c) If \(p(0)=1.7\), what is \(\lim _{t \rightarrow+\infty} p(t)\)?
(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:
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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