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A polluted pool has an initial concentration of bacteria of 10* part/m³, while the acceptable level is only 5 x 103 part/m³. The concentration of the bacteria will reduce as fresh water enter the pool. The differential equation that governs the concentration C of the pollutant as a function of time (in weeks) is given by: dC + 0.05C = 0, C(0) = 104 dt (i) Estimate the concentration of the pollutant after 15 weeks by taking a step size of 1 week. (ii) Find the absolute error if the exact solution of Q3(a)(i) is C(t) = 10*e-0.05t

A polluted pool has an initial concentration of bacteria of 10* part/m³, while the acceptable level is only 5 x 103 part/m³. The concentration of the bacteria will reduce as fresh water enter the pool. The differential equation that governs the concentration C of the pollutant as a function of time (in weeks) is given by: dC + 0.05C = 0, C(0) = 104 dt (i) Estimate the concentration of the pollutant after 15 weeks by taking a step size of 1 week. (ii) Find the absolute error if the exact solution of Q3(a)(i) is C(t) = 10*e-0.05t

Advanced Engineering Mathematics
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) A polluted pool has an initial concentration of bacteria of 104 part/m³, while the acceptable level is only 5 x 103 part/m³. The concentration of the bacteria will reduce as fresh water enter the pool. The differential equation that governs the concentration C of the pollutant as a function of time (in weeks) is given by: dC + 0.05C = 0, dt C(0) = 10* Estimate the concentration of the pollutant after 15 weeks by taking a step size of 1 week. (i) (ii) Find the absolute error if the exact solution of Q3(a)(i) is C(t) = 10*e-0.05t
Transcribed Image Text:(a) A polluted pool has an initial concentration of bacteria of 104 part/m³, while the acceptable level is only 5 x 103 part/m³. The concentration of the bacteria will reduce as fresh water enter the pool. The differential equation that governs the concentration C of the pollutant as a function of time (in weeks) is given by: dC + 0.05C = 0, dt C(0) = 10* Estimate the concentration of the pollutant after 15 weeks by taking a step size of 1 week. (i) (ii) Find the absolute error if the exact solution of Q3(a)(i) is C(t) = 10*e-0.05t
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