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(a)
value of k
size of population
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(1 point) Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal...
05.02. Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population...
05.02. Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6900. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP/dt=kP(1−P/K), determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k=......................., P(t)=..................... (b) How long will it...
(4 pts) Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal...
(4 pts) Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation determine the constant k, and then solve the equation to find an expression for the size of the population after years. k= P(t) = (b) How long will it...
6. Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population...
6. Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 8000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. (b) How long will it take for the population to increase to 4000?
Biologists stocked a lake with 300 fish and estimated the environmental carrying capacity to be 9700....
Biologists stocked a lake with 300 fish and estimated the environmental carrying capacity to be 9700. The number of fish doubled in the first year. a. Assume that the size of the fish population satisfies the logistic equation ), where t is measured in years. = KP Find an expression for the size of the population. Hint: Use partial fraction decomposition to solve for P. P = b. How long will it take for the population to increase to 4850...
4. 1-/2 Points) PRACTICE ANOTHER DETAILS SCALCCC4 7.5.010.MI. MY NOTES Biologists stocked a lake with 200...
4. 1-/2 Points) PRACTICE ANOTHER DETAILS SCALCCC4 7.5.010.MI. MY NOTES Biologists stocked a lake with 200 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 14,000. The number of fish tripled in the first year, (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the proutation after years. PC) (D) How long will it take for the population...
Some biologists decided to seed a lake with 800 trout. They estimated the carrying capacity of...
Some biologists decided to seed a lake with 800 trout. They estimated the carrying capacity of the lake to be 5,600 trout. By the end of year 3 they noticed that the population of trout had tripled. () Assuming the population follows the logistic model, calculate the relative growth rate k for an unconstrained environment k 0.536 Round your answer to 3 decimal places. (i) After how many years did the population in the lake reach 3,200 trout? Answer: Number...
Some biologists decided to seed a lake with 1,000 trout. They estimated the carrying capacity of...
Some biologists decided to seed a lake with 1,000 trout. They estimated the carrying capacity of the lake to be 4,000 trout. By the end of year 4 they noticed that the population of trout had tripled. (i) Assuming the population follows the logistic model, calculate the relative growth rate k for an unconstrained environment. k= Number Round your answer to 3 decimal places. (ii) After how many years did the population in the lake reach 2,500 trout? Answer: Number...
Please answer all parts in detail, thank you. Find the orthogonal trajectories of the family of...
Please answer all parts in detail, thank you.
Find the orthogonal trajectories of the family of curves y2 = kx5 Bilogists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish in that lake) to be 9000. The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after tyears.
Part B Please!! Scenario The population of fish in a fishery has a growth rate that...
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
Exercise 4: Assume that a population is governed by a logistic equation with carrying capacity K...
Exercise 4: Assume that a population is governed by a logistic equation with carrying capacity K intrinsic growth rate r, and initial population size K is subjected to constant effort harvesting: (a) Determine the population size, N(t) (b) Verify that if E< r, the population size will approach the positive steady state, Ni, the carrying capacity K if Erand if E>r, the population will approach the zero steady state, No, astoo. (c) Find the maximum sustainable yield of the population.
(4 pts) Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation determine the constant k, and then solve the equation to find an expression for the size of the population after years. k= P(t) = (b) How long will it...
6. Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 8000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. (b) How long will it take for the population to increase to 4000?
Biologists stocked a lake with 300 fish and estimated the environmental carrying capacity to be 9700. The number of fish doubled in the first year. a. Assume that the size of the fish population satisfies the logistic equation ), where t is measured in years. = KP Find an expression for the size of the population. Hint: Use partial fraction decomposition to solve for P. P = b. How long will it take for the population to increase to 4850...
4. 1-/2 Points) PRACTICE ANOTHER DETAILS SCALCCC4 7.5.010.MI. MY NOTES Biologists stocked a lake with 200 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 14,000. The number of fish tripled in the first year, (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the proutation after years. PC) (D) How long will it take for the population...
Some biologists decided to seed a lake with 800 trout. They estimated the carrying capacity of the lake to be 5,600 trout. By the end of year 3 they noticed that the population of trout had tripled. () Assuming the population follows the logistic model, calculate the relative growth rate k for an unconstrained environment k 0.536 Round your answer to 3 decimal places. (i) After how many years did the population in the lake reach 3,200 trout? Answer: Number...
Some biologists decided to seed a lake with 1,000 trout. They estimated the carrying capacity of the lake to be 4,000 trout. By the end of year 4 they noticed that the population of trout had tripled. (i) Assuming the population follows the logistic model, calculate the relative growth rate k for an unconstrained environment. k= Number Round your answer to 3 decimal places. (ii) After how many years did the population in the lake reach 2,500 trout? Answer: Number...
Please answer all parts in detail, thank you.
Find the orthogonal trajectories of the family of curves y2 = kx5 Bilogists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish in that lake) to be 9000. The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after tyears.
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
Exercise 4: Assume that a population is governed by a logistic equation with carrying capacity K intrinsic growth rate r, and initial population size K is subjected to constant effort harvesting: (a) Determine the population size, N(t) (b) Verify that if E< r, the population size will approach the positive steady state, Ni, the carrying capacity K if Erand if E>r, the population will approach the zero steady state, No, astoo. (c) Find the maximum sustainable yield of the population.
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