Populations that can be modeled by the modified logistic equation dP dt P(bP-a) can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.0015 and a = 0.18, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes. OT = a. Population will trend towards extinction b. Doomsday scenario: Population will exhibit unbounded growth in finite time a Initial population is 54 individuals b✓ Initial population is 283 individuals There is also a constant equilibrium solution for the population. Find this solution (note that the solution often is not a whole number, and hence unrealistic for population modeling). P(t) = 120 Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 283. T= P(t) Find the time I such that P(t) → ∞ as t → T. =
Populations that can be modeled by the modified logistic equation dP dt P(bP-a) can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.0015 and a = 0.18, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes. OT = a. Population will trend towards extinction b. Doomsday scenario: Population will exhibit unbounded growth in finite time a Initial population is 54 individuals b✓ Initial population is 283 individuals There is also a constant equilibrium solution for the population. Find this solution (note that the solution often is not a whole number, and hence unrealistic for population modeling). P(t) = 120 Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 283. T= P(t) Find the time I such that P(t) → ∞ as t → T. =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![Populations that can be modeled by the modified logistic equation
dP
dt
=
= P(bP – a)
can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial
population size. If b = 0.0015 and a = 0.18, use phase portrait analysis to determine which of the two
limiting behaviors will be exhibited by populations with the indicated initial sizes.
a. Population will trend towards extinction
b. Doomsday scenario: Population will exhibit unbounded growth in finite time
There is also a constant equilibrium solution for the population. Find this solution (note that the solution
often is not a whole number, and hence unrealistic for population modeling).
P(t) =
a Initial population is 54 individuals
Initial population is 283 individuals
=
T =
120
OF
Solve the modified logistic equation using the values of a and b given above, and an initial population of
P(0) = 283.
P(t) =
=
Find the time I such that P(t) → ∞ as t → T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54cb8c7a-f5c8-4f70-beb9-4c302d85da57%2F7cdb176d-f9d2-45d1-b521-8603f359586a%2Ffht0irc_processed.png&w=3840&q=75)
Transcribed Image Text:Populations that can be modeled by the modified logistic equation
dP
dt
=
= P(bP – a)
can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial
population size. If b = 0.0015 and a = 0.18, use phase portrait analysis to determine which of the two
limiting behaviors will be exhibited by populations with the indicated initial sizes.
a. Population will trend towards extinction
b. Doomsday scenario: Population will exhibit unbounded growth in finite time
There is also a constant equilibrium solution for the population. Find this solution (note that the solution
often is not a whole number, and hence unrealistic for population modeling).
P(t) =
a Initial population is 54 individuals
Initial population is 283 individuals
=
T =
120
OF
Solve the modified logistic equation using the values of a and b given above, and an initial population of
P(0) = 283.
P(t) =
=
Find the time I such that P(t) → ∞ as t → T.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 5 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)