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 byPN+1rPN(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 isSelect 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 theseO e. 50% of the pond's carrying capacity.

As per the question we are given the logistic growth model for a fish population. And we have to…

Answered: Assume there is a certain population of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

The formula for exponential growth is Q(t)3DQoekt. Q+= Q•e* a(0):150nc a Q L):50c °,95al 0,95k4 Qlう:63616.95 3OnCe Qcql=1362 Mcg 362 MCg -STaci)=63617 Mcg 150:Q0 1362=150et 9 k:0.55 8. Perform the indicated operations given A = [;B = and C = A 3D -31* 1 3 5. (b) 2B-C (a) AC+ B
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 =
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 120% per year. If the starting population is given by po = 500, then after one breeding season the population of the pond is given by P1 = Round your answer to the nearest integer.
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 8100. The number of fish doubled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP - kp(1-2). = 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 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 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.
A population grows according to the logistic growth model, with growth parameter r= 1.8. Starting with an initial population given by P = 0.6, complete parts (a) and (b). (a) Find the values of p₁ through P10- P₁ = ₁ P₂ = P3 = P4 = P5 P10 = P6= P7 = ₁ P8 = Pg = ₁ (Round to four decimal places as needed.) (b) What does the logistic model predict in the long term for this population? O A. The population settles into a two-period cycle with the following approximate percentages of the habitat's carrying capacity: 44.17% and 44.43%. OB. It stabilizes at about 44.44% of the habitat's carrying capacity. C. The species will become extinct. OD. The population settles into a four-period cycle with the following approximate percentages of the habitat's carrying capacity: 44.17%, 44.43%, 43.20%, 44.44%.
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.
the half life of caffeine in a healthy adult's bloodstream in 5.7 hours. suppose alex, a healthy adult, drinka a grande latte, which contains 150mg of caffeine, at 4pm. use the exponential decay model where t is the time since 4 pm measured in hours, k is exponential decay rate of caffeine and a9t) is the amount of caffeine in alex's bloodstream at time t
The bass population of a mountain lake was measured a year ago, and the lake was found to host 6,000 bass. If the current bass population is 10,500 and the bass grow according to a logistic growth model with carrying capacity 60,000, determine the growth constant k.k = What are the units of k? years2years−1 years plz show step by step 9 )
A colony of 120 wood frogs was introduced to a pond with a carrying capacity of C=300. The population grows according to the logistic growth model, with a growth parameter is r = 1.5. The logistic growth formula is: pN+1 = rpN(1-pN) a) Find the initial p-value: p0 = Answer b) Find the first p-value: p1 = Answer c) Find the second p-value: p2 = Answer
A study of Maryland's portion of Chesapeake Bay found the following information about stocks of market-sized oysters.† In 1994, the stocks were 218 million. (This is the number you will use for the initial population N(0).) The carrying capacity is 5089 million oysters. The intrinsic exponential growth rate is 0.274 per year. (a) Find a logistic model N(t) for the number, in millions, of market-sized oysters. Take t to be the time in years since 1994. (Rround all regression parameters to three decimal places.) N(t) = (b) Plot the graph of the model you found in part (a) over the first 20 years. (c) How many market-sized oysters does your model predict for 2007? Round your answer, in millions, to the nearest whole number. million oysters (d) The actual number of market-sized oysters was found to be 82 million. Use the Internet to find possible explanations for the reduced levels of oysters in Chesapeake Bay.
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 =

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS