A toxic chemical accidentally released into the environment from a metal processing plant degrades according to the law dQ = -0.04Q dt where t is measured in years. If the initial leak is of 60kg, a. Use the separation of variables method to find the amount remaining at any given time. b. Prove that the general solution found above can also generated using the integrating factor method. c. Find the amount remaining after 10 years.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
A toxic chemical accidentally released into the environment from a metal processing
plant degrades according to the law
dQ
= -0.04Q
dt
where t is measured in years. If the initial leak is of 60kg,
a. Use the separation of variables method to find the amount remaining at any given
time.
b. Prove that the general solution found above can also generated using the
integrating factor method.
c. Find the amount remaining after 10 years.
Transcribed Image Text:A toxic chemical accidentally released into the environment from a metal processing plant degrades according to the law dQ = -0.04Q dt where t is measured in years. If the initial leak is of 60kg, a. Use the separation of variables method to find the amount remaining at any given time. b. Prove that the general solution found above can also generated using the integrating factor method. c. Find the amount remaining after 10 years.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning