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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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.
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