5) The population of rabbits on a small island is modeled by the differential equation time is measured in years. = 1.2P – (3 × 10-4)P², where i) Find all of the fixed points of this equation, and draw a phase diagram. Classify each fixed point as stable or unstable. ii) What is the carrying capacity of the island? iii) Suppose that at t = 0, the population of rabbits is 1000. Find the population as a function of time, and determine when the population will reach 90% of the carrying capacity. (Note: you may refer to the logistic general solution given at the bottom of the page)

5) The population of rabbits on a small island is modeled by the differential equation time is measured in years. = 1.2P – (3 × 10-4)P², where i) Find all of the fixed points of this equation, and draw a phase diagram. Classify each fixed point as stable or unstable. ii) What is the carrying capacity of the island? iii) Suppose that at t = 0, the population of rabbits is 1000. Find the population as a function of time, and determine when the population will reach 90% of the carrying capacity. (Note: you may refer to the logistic general solution given at the bottom of the page)

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

dP
dt
(3 × 10-4)P², where
5) The population of rabbits on a small island is modeled by the differential equation
time is measured in years.
1.2P -
i)
Find all of the fixed points of this equation, and draw a phase diagram. Classify each fixed point as stable or
unstable.
ii)
What is the carrying capacity of the island?
iii) Suppose that at t
when the population will reach 90% of the carrying capacity. (Note: you may refer to the logistic general solution
given at the bottom of the page)
0, the population of rabbits is 1000. Find the population as a function of time, and determine

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