The initial value problem modeling the number of fish in a stocked pond after t years isdy = = .08y — b, y(0) = 400. b is greater than zero and represents the harvesting rate.dta) Find the value of b which causes a non-zero steady state solution.b) Solve the initial value problem.c) What is the steady state solution if b is smaller than the value found in part a of thisproblem?d) What is the steady state solution if b is larger than the value found in part a of this problem?

Given: The given initial value problem of the number of fish in a pond after t years is:…

Answered: The dy initial value problem modeling…

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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A new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.
Money in a bank account at time t can be modeled by fip = ry + D where the constant r is related to the interest rate and the constant D is the related to regular deposits at a constant rate. (a) Solve the DE for any initial condition where r = .05 and D = 5000 and t is in years. (Side note: this is NOT the same as annual deposits of $5000) (b) If the initial amount is $0, solve for C. (c) For the answer in (b) how long will it take to reach $1 million?
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A): What is the carrying capacity of the population? B): What is the total population at the moment the population is growing at the fastest rate? Please find part A and B
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