Consider the differential equation 
a) Assume that 
b) Assume that 
Can I have a step-by-step walkthrough on how to solve these two. I need to know how to graph especially. Please don't assume anything, explain it all. It would be greatly appreciated to have someone answer my question in it's entirety.
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Consider the differential equation for , which models a population of fish with harvesting that...
Consider the differential equation . for x20, which models a population of fish with harvesting that...
Consider the differential equation . for x20, which models a population of fish with harvesting that is governed by the logistic equation and a number of fish H caught and removed every unit if time (harvesting). Here the parameters r, K, and H are all positive. a Assume tht Heate e. 4 rk If H <テ, what levels ofinitial fish population lead to a fish population which does not die out? Assume that H>.What happens to the population of fish...
step by step please 4. Suppose that the logistic equation dt Pla -bP) models a population of fish in a lake after t months during which no fishing occurs. What is the limiting population for this...
step by step please
4. Suppose that the logistic equation dt Pla -bP) models a population of fish in a lake after t months during which no fishing occurs. What is the limiting population for this fish population? suppose that, because of fishing, fish are removed from the lake at a rate proportional to the existing fish population. i. Write a differential equation that describes this situation. ii. Show that if the constant of proportionality for the harvest of fish,...
A population of fish is modeled by the logistic equation modified to account for harvesting ??/??...
A population of fish is modeled by the logistic equation modified to account for harvesting ??/?? = .25? (1 − (?/4) ) - a or equivalently ??/?? = − (1/16) ?^2 + (1/4) ? - a 1.) What will happen to the size of the population in the long run? If your answer depends on the initial population size (hint – it should!), be sure to include all possible scenarios. 2.) Use MATLAB to solve this differential equation. (Yes, it...
Q2- Fish Population In this question, we will use differential equations to study the fish population...
Q2- Fish Population In this question, we will use differential equations to study the fish population in a certain lake. An acceptable model for fish population change should take into account the birth rate, death rate, as well as harvesting rate Let P(t) denote the living fish population (measured in tonnes) at time t (measured in year) Then the net rate of change of the fish population in tonnes of fish per year is P'(t): P'(t) birth rate - death...
A fish hatchery employed a mathematician to design a model to predict the population size of fish...
What are the solutions to the following diff eq’s?
A fish hatchery employed a mathematician to design a model to predict the population size of fish that the hatchery can expect to find in their pond at any given time. The mathematical model that the mathematician created is: dP dt 25 (a) Draw a one dimensional phase portrait of the autonomous differential equa- tion. What does this differential equation predict for future fish populations for various initial conditions? Describe the...
A population of fish is modeled by the logistic equation modified to account for harvesting: de...
A population of fish is modeled by the logistic equation modified to account for harvesting: de = 25p (1-) -a or equivalently top2 + 3p-a 1. What are the equilibrium solutions? Note: your answer(s) should be expressed in terms of a 2. Determine the range of values of a for which this model has 2 different equilibrium values. When does it have 1 equilibrium? O equilibria? Carefully interpret each of these scenarios in the context of this model. 3. Suppose...
In this problem we assume that fish are caught at a constant rate h independent of...
In this problem we assume that fish are caught at a constant
rate h independent of the size of the fish population. Then y
satisfies
7. (10 pts.) In this problem we assume that fish are caught at a constant rate h independent of the size of the fish population. Then y satisfies =r(1 - y/K)y-h dt a) If h <rk/4, show that the above equation has two equilibrium points yı and y2 with yi < y2; determine these points....
Which of the following is the solution to the differential equation with the initial condition y(1)...
Which of the following is the solution to the differential
equation
with the initial condition y(1) = -1/2
A.
B.
C.
D.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
I need help with question #3 When there is no fishing, the growth of a population of clown fish is governed by the following differential equation: dy dt 200 where y is the number of fish at time t in...
I need help with question
#3
When there is no fishing, the growth of a population of clown fish is governed by the following differential equation: dy dt 200 where y is the number of fish at time t in years. 1. Solve for the equilibrium value(s) and determine their stability. Create a slope field for this differential equation. Use the slope field to sketch solutions for various initial values. 2. 3. Summarize the behavior of the solutions and how...
3. Suppose that th ite population y()of a certain kind of fish is given by the...
3. Suppose that th ite population y()of a certain kind of fish is given by the logistic equation without catching fish: and now we will catch the fish at a rate Hy (H< A). Find an equilibrium solution y(t) as too and what if there were no fishing? (20 points) dy Ay_By2 (A, B>0),
Consider the differential equation . for x20, which models a population of fish with harvesting that is governed by the logistic equation and a number of fish H caught and removed every unit if time (harvesting). Here the parameters r, K, and H are all positive. a Assume tht Heate e. 4 rk If H <テ, what levels ofinitial fish population lead to a fish population which does not die out? Assume that H>.What happens to the population of fish...
step by step please
4. Suppose that the logistic equation dt Pla -bP) models a population of fish in a lake after t months during which no fishing occurs. What is the limiting population for this fish population? suppose that, because of fishing, fish are removed from the lake at a rate proportional to the existing fish population. i. Write a differential equation that describes this situation. ii. Show that if the constant of proportionality for the harvest of fish,...
Q2- Fish Population In this question, we will use differential equations to study the fish population in a certain lake. An acceptable model for fish population change should take into account the birth rate, death rate, as well as harvesting rate Let P(t) denote the living fish population (measured in tonnes) at time t (measured in year) Then the net rate of change of the fish population in tonnes of fish per year is P'(t): P'(t) birth rate - death...
What are the solutions to the following diff eq’s?
A fish hatchery employed a mathematician to design a model to predict the population size of fish that the hatchery can expect to find in their pond at any given time. The mathematical model that the mathematician created is: dP dt 25 (a) Draw a one dimensional phase portrait of the autonomous differential equa- tion. What does this differential equation predict for future fish populations for various initial conditions? Describe the...
A population of fish is modeled by the logistic equation modified to account for harvesting: de = 25p (1-) -a or equivalently top2 + 3p-a 1. What are the equilibrium solutions? Note: your answer(s) should be expressed in terms of a 2. Determine the range of values of a for which this model has 2 different equilibrium values. When does it have 1 equilibrium? O equilibria? Carefully interpret each of these scenarios in the context of this model. 3. Suppose...
In this problem we assume that fish are caught at a constant
rate h independent of the size of the fish population. Then y
satisfies
7. (10 pts.) In this problem we assume that fish are caught at a constant rate h independent of the size of the fish population. Then y satisfies =r(1 - y/K)y-h dt a) If h <rk/4, show that the above equation has two equilibrium points yı and y2 with yi < y2; determine these points....
Which of the following is the solution to the differential
equation
with the initial condition y(1) = -1/2
A.
B.
C.
D.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
I need help with question
#3
When there is no fishing, the growth of a population of clown fish is governed by the following differential equation: dy dt 200 where y is the number of fish at time t in years. 1. Solve for the equilibrium value(s) and determine their stability. Create a slope field for this differential equation. Use the slope field to sketch solutions for various initial values. 2. 3. Summarize the behavior of the solutions and how...
3. Suppose that th ite population y()of a certain kind of fish is given by the logistic equation without catching fish: and now we will catch the fish at a rate Hy (H< A). Find an equilibrium solution y(t) as too and what if there were no fishing? (20 points) dy Ay_By2 (A, B>0),
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