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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??

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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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??
Transcribed Image Text: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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