A polluted pool has an initial concentration of bacteria of 10* part/m³, while the a) 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) = 104 (i) Estimate the concentration of the pollutant after 15 weeks by taking a step

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

please send the answer within one hour

(а)
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*
(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
(a)(i) is
C(t) = 10ªe-0.05t
Transcribed Image Text:(а) 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* (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 (a)(i) is C(t) = 10ªe-0.05t
Expert Solution
steps

Step by step

Solved in 5 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,