12 In order to save an endangered species, it has been decided to release 40 animals on an island wherethere are no predators. The maximum number that can survive on the island is called the carryingcapacity, which is 1000. It is assumed that the population N of these animals at time t years after releasefits the logistic growth equationdN= kN (1000dtN),for some constant k.10001+1000 – N1a Show thatN(1000 – N)b Use the result of part a to find the general solution of the logistic growth equation.c Determine the arbitrary constant by applying the initial condition N (0)40, then simplify thefunction.d Given that the population of animals after 1 year was 80, find the value of k correct to four significantfigures.e What will the population be after 5 years, correct to the nearest whole number?

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Answered: 12 In order to save an endangered…

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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