Populations that can be modeled by the modified logistic equationdPdt== P(bP – a)can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initialpopulation size. If b = 0.0015 and a = 0.18, use phase portrait analysis to determine which of the twolimiting behaviors will be exhibited by populations with the indicated initial sizes.a. Population will trend towards extinctionb. Doomsday scenario: Population will exhibit unbounded growth in finite timeThere is also a constant equilibrium solution for the population. Find this solution (note that the solutionoften is not a whole number, and hence unrealistic for population modeling).P(t) =a Initial population is 54 individualsInitial population is 283 individuals=T =120OFSolve the modified logistic equation using the values of a and b given above, and an initial population ofP(0) = 283.P(t) ==Find the time I such that P(t) → ∞ as t → T.

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Answered: Populations that can be modeled by the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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 1600 fish. Absent constraints, the population would grow by 230% per year.
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.
Suppose a species of fish in a particular lake has a population that is modeled bythe logistic population model with growth rate k, carrying capacity N, and time tmeasured in years. Adjust the model to account for each of the following situations. * One hundred fish are harvested each year.* One-third of the fish population is harvested annually.* The number of fish harvested each year is proportional to the square root of thenumber of fish in the lake. I was hoping to compare my answer to yours because I am a little confused if I did it right. Thank you for your time and effort.
A population of fish is living in an environment with limited resources. This environment can only support the population if it contains no more than M fish (otherwise some fish would starve due to an inadequate supply of food, etc.). There is considerable evidence to support the theory that, for some fish species, there is a minimum population m such that the species will become extinct if the size of the population falls below m. Such a population can be modelled using a modified logistic equation: dP =(1-)(-) m dt M
Consider the plot of the total number E of Ebola cases in West Africa reported to the Centers for Disease Control and Prevention from April 1, 2014, through December 1, 2015. D +|+|||||||||||||||| ► Ebola Cases in West Africa E = A logistic fit for these data is given by 27,841.42 1 + 134.65-0.646 where t is the time in months since April 1, 2014. Below, we have added the graph of this model. +-+|||||||||||||||||| ► Logistic Graph Added (a) Does the first plot, "Ebola Cases in West Africa," show a continuing epidemic or a health crisis that is under control by December 2015? Because the data points appear to be [leveling off ✔✔✔, they show a health crisis that is under control (b) According to the model, what was the total number of cases when the disease was spreading at the fastest rate? Round your answer to the nearest whole number. 27021.61 x cases (c) Use the crossing-graphs method to determine when the disease was growing at the fastest rate. Round your answer, in months after…
Nitrogen dioxide, NO₂, is an air pollutant resulting from burning fossil fuels in cars and power plants. The following table shows the decrease in the national average of the concentration in parts per billion (ppb) of NO₂ for selected years. Year 2014 40.8107 2015 2016 2017 2018 39.7886 38.7972 37.8209 36.8752 NO₂ (ppb) Use exponential regression to find an exponential decay function for the concentration, C, of NO₂ t years after 2014. Round constants to the nearest ten-thousandth. c-40.8114 (0.9750) Use the model to predict the concentration of NO₂ (in ppb) in 2045. Round to the nearest whole number. 21 x ppb
Nitrogen dioxide, NO2, is an air pollutant resulting from burning fossil fuels in cars and power plants. The following table shows the decrease in the national average of the concentration in parts per billion (ppb) of NO2 for selected years. Year 2014 2015 2016 2017 2018 NO2 (ppb) 40.8107 39.7886 38.7972 37.8209 36.8752 Use exponential regression to find an exponential decay function for the concentration, C, of NO2 t years after 2014. Round constants to the nearest ten-thousandth. C = Use the model to predict the concentration of NO2 (in ppb) in 2050. Round to the nearest whole number. ? ppb

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