A pond initially contains 8,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.06 grams of this chemical per gallon flows into the pond at a rate of 500 . The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly h 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. Use q as q (t). Do not use thousands separator in the answer field. dq grams hour dt (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 = Number grams
A pond initially contains 8,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.06 grams of this chemical per gallon flows into the pond at a rate of 500 . The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly h 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. Use q as q (t). Do not use thousands separator in the answer field. dq grams hour dt (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 = Number grams
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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Transcribed Image Text:A pond initially contains 8,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.06 grams of this chemical per gallon flows
gal
into the pond at a rate of 500
h
distributed throughout the pond.
The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly
(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. Use q as
q (t).
Do not use thousands separator in the answer field.
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?
= Number
grams
The limiting amount.
(Click for List)
depend on the amount that was present initially.
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