Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximalpopulation for the fish of that species in that lake) to be 8100. The number of fish doubled inthe first year.(a) Assuming that the size of the fish population satisfies the logistic equationdP - kp(1-2).=dtdetermine the constant k, and then solve the equation to find an expression for the size of thepopulation after t years.k -P(t) =(b) How long will it take for the population to increase to 4050 (half of the carrying capacity)?It will take 3.575 years.

Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population…

Answered: Biologists stocked a lake with 500 fish…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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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 9700. The number of fish doubled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation - KP (1-P) dP dt " 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 take for the population to increase to 4850 (half of the carrying capacity)? It will take years.
For a Pacific halibut population, the value of r is 0.71 per year, and the environmental carrying capacity is 89 thousand tons of fish.† (a) Find the time it takes the population to grow from the optimum yield level to 87% of carrying capacity if the number b in the logistic growth equation is 1.5. (Round your answer to three decimal places.) yr(b) Find the time it takes the population to grow from the optimum yield level to 87% of carrying capacity if the number b in the logistic growth equation is 4.8. (Round your answer to three decimal places.) yr
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. The growth parameter for this type of fish is r = 3.0. The logistic growth formula is given by PN+1 rPN(1-PN) If originally the pond is stocked to 50% of its carrying capacity, then the population of the pond after the second breeding season is Select one: a. 25% of the pond's carrying capacity. b. 56.25% of the pond's carrying capacity. c. 75% of the pond's carrying capacity. d. none of these O e. 50% of the pond's carrying capacity.
Assume that the population of a town can be modeled by the logistic equation dP/dt = kP(1000 - P). If this town's population was 800 five years ago and is 850 this year, what is its population expected to be five years from now? Round your answer to the nearest integer.
Assume 100 snails originally have the virus and that in early stages the number of snails infected is increasing approximately exponentially, with a continuous growth rate of 0.02. Assume further that in the long run, they estimate approximately 5300 snails will be infected. The number of snails infected after t hours after infection began is modeled by a logistic function: P=L1+Ce−kt What is the value of t when the rate at which snails are becoming infected peaks? Select the closest value.
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=300, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
A endangered species is released into a park. The population of an endangered species is expected to follow the logistic model p(t)= 810/1+8e-188t . Where t is measured in mionths. a. How many endangered species were released into the park? b. How many endangered species will there be in 5 months? c. As time goes by, what appears to be the maximum population in the park?
A tree farm starts with ten trees. Tree growth is expected to follow logistic growth with a first-order growth rate constant of r = 0.16 yr ' to a maximum of 8,000 trees. Write the equation that relates the number of trees (N) to time (1). What are the values of No, r, and K? Plot the number of trees over time if no harvesting occurs. Go out to about 70 years. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY? Determine the standing crop. (The standing crop is the number of trees at steady state when harvesting at the MSY.)
The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?
Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP = kp (1-P). (1-²), kP dt 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 take for the population to increase to 2500 (half of the carrying capacity)? It will take years.
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 2000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1200 fish. Absent constraints, the population would grow by 110% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =

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