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A pond initially contains 6,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.05 grams of this chemical per gallon flows into the pond at a rate of 500 gal/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. (a) Write a differential equation for the amount of chemical in the pond at any time. Let q(t) denote the amount of chemical in the pond at time t. NOTE: Use q as q(t). dą grams dt hour (b) How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? 9 = grams The limiting amount Choose one▼ depend on the amount that was present initially.

A pond initially contains 6,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.05 grams of this chemical per gallon flows into the pond at a rate of 500 gal/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. (a) Write a differential equation for the amount of chemical in the pond at any time. Let q(t) denote the amount of chemical in the pond at time t. NOTE: Use q as q(t). dą grams dt hour (b) How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? 9 = grams The limiting amount Choose one▼ depend on the amount that was present initially.

Advanced Engineering Mathematics
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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Please provide me the correct answer I am posting this question for second time, so i request I need correct answer please.. Needed both parts a and b please
A pond initially contains 6,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.05 grams of this chemical per gallon flows into the pond at a rate of 500 gal/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. (a) Write a differential equation for the amount of chemical in the pond at any time. Let q(t) denote the amount of chemical in the pond at time t. NOTE: Use q as q(t). dą grams dt hour (b) How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? q = grams The limiting amount Choose one▼ depend on the amount that was present initially.
Transcribed Image Text:A pond initially contains 6,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.05 grams of this chemical per gallon flows into the pond at a rate of 500 gal/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. (a) Write a differential equation for the amount of chemical in the pond at any time. Let q(t) denote the amount of chemical in the pond at time t. NOTE: Use q as q(t). dą grams dt hour (b) How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? q = grams The limiting amount Choose one▼ depend on the amount that was present initially.
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