6. A population of fish is living in an environment with limited resources. This environment canonly support the population if it contains no more than M fish (otherwise some fish wouldstarve due to an inadequate supply of food, etc.). There is considerable evidence to supportthe theory that, for some fish species, there is a minimum population m such that the specieswill become extinct if the size of the population falls below m. Such a population can bemodelled using a modified logistic equation:dP= kPdt(1-4)(--#)PM3(a) Use the differential equation to show that any solution is increasing if m < P < M anddecreasing if 0 < P < m.(b) For the case where k = 1, M = 100, 000 and m = 10, 000, draw a direction field and useit to sketch several solutions for various initial populations. What are the equilibriumsolutions?(c) One can show thatk(M-m)M(Po – m)et— т(Ро — М)MP(t) =k(M-m)(Ро — т)е мt— (Ро — М)is a solution with initial population P(0) = Po. Use this to show that, if P(0) < m, thenthere is a time t at which P(t) = 0 (and so the population will be extinct).

Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

6. 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 = kP dt (1-4)(-). M 3 (a) Use the differential equation to show that any solution is increasing if m < P < M and decreasing if 0 < P

6. 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 = kP dt (1-4)(-). M 3 (a) Use the differential equation to show that any solution is increasing if m < P < M and decreasing if 0 < P

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

See similar textbooks