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A pond initially contains 6000 gallons of water and 900 grams of an undesirable chemical. Water containing 0.37 grams of this chemical per gallon flows nto the pond at a rate of 57 gallons per hour. Water flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Write a differential equation for the amount of chemical, c (in grams), in the pond at time t (in hours).

A pond initially contains 6000 gallons of water and 900 grams of an undesirable chemical. Water containing 0.37 grams of this chemical per gallon flows nto the pond at a rate of 57 gallons per hour. Water flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Write a differential equation for the amount of chemical, c (in grams), in the pond at time t (in hours).

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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A pond initially contains 6000 gallons of water and 900 grams of an undesirable chemical. Water containing 0.37 grams of this chemical per gallon flows into the pond at a rate of 57 gallons per hour. Water flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Write a differential equation for the amount of chemical, c (in grams), in the pond at time t (in hours). dc dt = How much of the chemical will be in the pond after a very long time? lim c(t) = = t→∞ grams
Transcribed Image Text:A pond initially contains 6000 gallons of water and 900 grams of an undesirable chemical. Water containing 0.37 grams of this chemical per gallon flows into the pond at a rate of 57 gallons per hour. Water flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Write a differential equation for the amount of chemical, c (in grams), in the pond at time t (in hours). dc dt = How much of the chemical will be in the pond after a very long time? lim c(t) = = t→∞ grams
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