Consider the differential equation dp P(p - 1) (2— р) dt 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],
Consider the differential equation dp P(p - 1) (2— р) dt 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],
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
(c), (d), and (e)
![Consider the differential equation
dp
Р(p — 1) (2 — р)
dt
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,+ p(t)?
(c) If p(0) = 1.7, what is lim,→+ P(t)?
(d) If p(0) = 0.8, what is lim,→+∞ p(t)?
(e) Can a population of 900 ever increase to 1100?
→+00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff57c5c9b-acb3-4a3d-a39b-55eeff7ee4ad%2F0a3861e2-6db2-4134-bd97-d8ba3eee95e4%2Fc02d887_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the differential equation
dp
Р(p — 1) (2 — р)
dt
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,+ p(t)?
(c) If p(0) = 1.7, what is lim,→+ P(t)?
(d) If p(0) = 0.8, what is lim,→+∞ p(t)?
(e) Can a population of 900 ever increase to 1100?
→+00
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