To better understand the population of certain animal species scientists have kept them in a closed and controlled environment. In this environment, the population of the species follows the following law: dx/dt = kx − λx^2 where time is in years, and k = 0.03, λ = 3(10)^−8 . a) The lead scientist has tasked you to find out a formula to calculate population in future years, given that population in 1980 is 200,000. b) Using the formula from part a, calculate the population in year 2000. c) Find the limiting value of the population as time approaches infinity (t → ∞).
To better understand the population of certain animal species scientists have kept them in a closed and controlled environment. In this environment, the population of the species follows the following law: dx/dt = kx − λx^2 where time is in years, and k = 0.03, λ = 3(10)^−8 . a) The lead scientist has tasked you to find out a formula to calculate population in future years, given that population in 1980 is 200,000. b) Using the formula from part a, calculate the population in year 2000. c) Find the limiting value of the population as time approaches infinity (t → ∞).
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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To better understand the population of certain animal species scientists have
kept them in a closed and controlled environment. In this environment, the
population of the species follows the following law:
dx/dt = kx − λx^2
where time is in years, and k = 0.03, λ = 3(10)^−8
.
a) The lead scientist has tasked you to find out a formula to calculate
population in future years, given that population in 1980 is 200,000.
b) Using the formula from part a, calculate the population in year 2000.
c) Find the limiting value of the population as time approaches infinity (t →
∞).
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