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 places.)
yr
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A small lake 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...
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.)...
A species of fish was added to a lake. The population size P(t) of this species...
A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. P(t)= 1200 -0.42t 1+ 3e Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary. Initial population size: fish Population size after 9 years: fish...
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...
of this species can be modeled by the following function, where is the number of years...
of this species can be modeled by the following function, where is the number of years A species of fish was added to a lake. The population size P time the species was added to the lake. 2000 PC- 1+7-021 Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary Initial population size: fish Population size after 9 years: fish x 5 ? Let o...
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?
Suppose that the population of a species of fish (in thousands) is modeled by f(?) =...
Suppose that the population of a species of fish (in thousands) is modeled by f(?) = x+10/0.5x2+1, where x ≥ 0 is in years. a. Sketch a graph of the function on the interval [0,12] x [0,12]. Label and scale your axes. b. What is the horizontal asymptote? c. What is the significance of the horizontal asymptote? d. What is the initial population of fish? e. What is the population of fish after 5 years? f. When is the population...
Consider a lake that is stocked with walleye pike and where population of pike is governed...
Consider a lake that is stocked with walleye pike and where population of pike is governed by the logistic equation P'= 0.1P(1-10 where time is measured in days and P in thousands of fish. Suppose that fishing is started in this lake and that 1o0 fish are removed each day. (a) Modify the logistic model to accurately account for the fishing. b) Find and classify the equilibrium points for your model. (c) Use qualitative analysis to discuss the fate of...
(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...
(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...
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...
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.)...
A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. P(t)= 1200 -0.42t 1+ 3e Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary. Initial population size: fish Population size after 9 years: fish...
of this species can be modeled by the following function, where is the number of years A species of fish was added to a lake. The population size P time the species was added to the lake. 2000 PC- 1+7-021 Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary Initial population size: fish Population size after 9 years: fish x 5 ? Let o...
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?
Consider a lake that is stocked with walleye pike and where population of pike is governed by the logistic equation P'= 0.1P(1-10 where time is measured in days and P in thousands of fish. Suppose that fishing is started in this lake and that 1o0 fish are removed each day. (a) Modify the logistic model to accurately account for the fishing. b) Find and classify the equilibrium points for your model. (c) Use qualitative analysis to discuss the fate of...
(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...
(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...
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...
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