The logistic equation for the population p (in thousands) at time t of a certain species is given by dp = = p(2 − p), - p> 0. dt 1. Sketch the direction field, either by hand or with the help of a graphical calculator. Use the direction field to answers the following questions. = 3, what can you say about the limiting a. If the initial population is 3000 that is, p(0) population lim p(t)? t-x b. Can a population of 1000 ever decline to 500? c. Can a population of 1000 ever increase to 3000? 2. Solve the ODE.
The logistic equation for the population p (in thousands) at time t of a certain species is given by dp = = p(2 − p), - p> 0. dt 1. Sketch the direction field, either by hand or with the help of a graphical calculator. Use the direction field to answers the following questions. = 3, what can you say about the limiting a. If the initial population is 3000 that is, p(0) population lim p(t)? t-x b. Can a population of 1000 ever decline to 500? c. Can a population of 1000 ever increase to 3000? 2. Solve the ODE.
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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Ordinary differential equation
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Transcribed Image Text:The logistic equation for the population p (in thousands) at time t
of a certain species is given by
dp
dt
=p(2-p),
P>0.
1. Sketch the direction field, either by hand or with the help of a graphical calculator.
Use the direction field to answers the following questions.
a. If the initial population is 3000 that is, p(0) = 3, what can you say about the limiting
population
lim p(t)?
t→∞
b. Can a population of 1000 ever decline to 500?
c. Can a population of 1000 ever increase to 3000?
2. Solve the ODE.
1
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