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Biologists stocked a lake with 300 fish and estimated the environmental carrying capacity to be 9700....
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...
(1 point) Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal...
(1 point) 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 5500. The number of fish doubled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP dt - 2P (1-1) determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k= 0.7985...
(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?
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...
A small lake is stocked with a certain species of fish. The fish population is modeled...
A small lake is stocked with a certain species of fish. The fish population is modeled by the function P = 12 1 + 4e−0.4t where P is the number of fish in thousands and t is measured in years since the lake was stocked. (a) Find the fish population after 4 years. (Round your answer to the nearest whole fish.) fish (b) After how many years will the fish population reach 6000 fish? (Round your answer to two decimal...
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.
A small take is stocked with a certain species of fish. The fish population is modeled...
A small take is stocked with a certain species of fish. The fish population is modeled by the function P- 14 1+ 4e -0.80 where P is the number of fish in thousands and t is measured in years since the lake was stocked. (6) Find the fish population after 3 years. (Round your answer to the nearest whole fish) fish (1) After how many years will the fish population reach 7000 fish? (Round your answer to two decimal places.)...
(1 point) 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 5500. The number of fish doubled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP dt - 2P (1-1) determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k= 0.7985...
(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?
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.
A small take is stocked with a certain species of fish. The fish population is modeled by the function P- 14 1+ 4e -0.80 where P is the number of fish in thousands and t is measured in years since the lake was stocked. (6) Find the fish population after 3 years. (Round your answer to the nearest whole fish) fish (1) After how many years will the fish population reach 7000 fish? (Round your answer to two decimal places.)...
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