(i) the equation to model the population. (ii) the population after 5 years. (iii) how long it will take the population to double.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Q5 (a) A population of a village grows proportion to its current population. The initial
population is 10,000 and grows 9% per year. This can be modeled
dP
= 0.09 P
dt
Determine
(i) the equation to model the population.
(ii) the population after 5 years.
(iii) how long it will take the population to double.
(b) A forced system is given by:
my' + ny' + ky = 10cos (2x)
Solve for the steady state solution in the case where m = 1, n= 3, and k = 2.
Transcribed Image Text:Q5 (a) A population of a village grows proportion to its current population. The initial population is 10,000 and grows 9% per year. This can be modeled dP = 0.09 P dt Determine (i) the equation to model the population. (ii) the population after 5 years. (iii) how long it will take the population to double. (b) A forced system is given by: my' + ny' + ky = 10cos (2x) Solve for the steady state solution in the case where m = 1, n= 3, and k = 2.
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