A pond contains 2740 L of pure water and an uknown amount of an undesirable chemical. Water contaninig 0.01 kg of this chemical per liter flows into the pond at a rate of 8 L/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Let Q(t) be the amount of chemical (in kg) in the pond at time t hours. (a) Write a differential equation for the amount of chemical i the pond? at any time time (enter Q for Q(t): dQ dt (b) How much chemical will be in the pond after a long time? Q∞ = (kg) (c) Does the limiting value in part (b) depend on the amount that was present initially??

A pond contains 2740 L of pure water and an uknown amount of an undesirable chemical. Water contaninig 0.01 kg of this chemical per liter flows into the pond at a rate of 8 L/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Let Q(t) be the amount of chemical (in kg) in the pond at time t hours. (a) Write a differential equation for the amount of chemical i the pond? at any time time (enter Q for Q(t): dQ dt (b) How much chemical will be in the pond after a long time? Q∞ = (kg) (c) Does the limiting value in part (b) depend on the amount that was present initially??

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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Question

A pond contains 2740 L of pure water and an uknown amount of an undesirable chemical. Water contan inig 0.01 kg of this chemical per liter flows into the pond at a rate of 8 L/h. The mixture flows out at the
same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond.
Let Q(t) be the amount of chemical (in kg) in the pond at time t hours.
(a) Write a differential equation for the amount of chemical in the pond?
at any time time (enter Q for Q(t):
dQ
dt
=
(b) How much chemical will be in the pond after a long time?
20⁰ =
(kg)
(c) Does the limiting value in part (b) depend on the amount that was present initially??

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