Q3 (a) 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, dt C(0) = 10* 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 -0.05t
Q3 (a) 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, dt C(0) = 10* 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 -0.05t
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
numerical
![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:
Q3
(a)
dC
+ 0.05C = 0,
C(0) = 10+
dt
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd114f843-7475-47ee-b275-010efc25d7f2%2F854c64ec-7803-4d1d-9d2c-51fce8bf233a%2F6dhzrj3_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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:
Q3
(a)
dC
+ 0.05C = 0,
C(0) = 10+
dt
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
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)