🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →
Log in
Calculus
1
answer
0
watching
271
views
8 Jun 2020

The fox and rabbit follow the predator-prey relationship in the forest. The population growth for both species is represented by Lotka-Volterra set of differential equation,

Rabbit :                    where a=0.4 and b=0.05

Fox :                              where c=0.2 and d= 0.005

 ‘a’ is the growth rate of rabbit population and ‘b’ is predation rate. Factor ‘c’ represents the mortality rate of fox and ‘d’ as growth of fox with predation. 

Which is of the following slope fields plot represents the variation of fox population with rabbit population if the initial population of rabbit and fox is 20 and 4 respectively?

 

Booster class
Calculus 2
Skill
Sketch slope fields
Watch
1
answer
0
watching
271
views

For unlimited access to Homework Help, a Homework+ subscription is required.

24 Jul 2020

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share

Related textbook solutions

Calculus
4 Edition,
Rogawski
ISBN: 9781319050733
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
CALCULUS:EARLY TRANSCENDENTALS
4 Edition,
Rogawski
ISBN: 9781319050740

Related questions

 In a natural habitat, wolf and rabbit form a predator prey relationship and the population growth of both species is governed by Lotka Volterra equation. The relation is given as,

Rabbit :

 

Wolf :

where, a is growth rate of rabbit population

b is predation rate

c is the death rate of wolf population

d is growth rate due to predation

As observed in the habitat, single wolf consumes multiple rabbits in a day. What condition must the equations satisfy to reflect this observation?

 

The local pond is filled with phytoplankton with squids as their natural predators to maintain the population growth of phytoplankton. The Lotka-Volterra equation describes predator prey relationship as:

 

Phytoplankton :

 

Squids :

The rate of population growth of phytoplankton and squids is given by above equation with ‘a’ is the growth rate of phytoplankton and ‘b’ is predation rate. Factor ‘c’ represents the mortality rate of squids and ‘d’ as growth rate of squids with predation.

Industrial effluent is being discharged into the lake and is toxic to both species, but directly consumed by phytoplankton only. If squids start consuming toxic borne plankton, the population growth rate will change. What pair of modified equations describe this scenario? Consider ‘x’ as toxicity rate common to both species.

 

 If two predators with one prey occurs in natural habitat, the Lotka Volterra equation for the population growth is given as

The ‘a’ is growth rate of prey, ‘p1’ is predation rate of predator 1 and ‘p2’ is predation rate of predator 2. ‘b’ is the death rate of predator 1 and ‘c’ is the death rate of predator 2. ‘d1’ and ‘d2’ are the growth rate of both predators with predation. If death rate of predator 1 is greater than predator 2 (b>c), then which species will go extinct as time tends to infinity (t→∞)?

 

Weekly leaderboard

Home
Homework Help 3,900,000
Calculus 630,000
Start filling in the gaps now
Log in