A pond initially contains 6,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.03 grams of this chemical per gallon flows into the pond at a rate of 300 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). dq 9-0.05 qt dt grams hour X (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? ?=180000 The limiting amount does not grams 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 0.03 grams of this chemical per gallon flows into the pond at a rate of 300 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). dq 9-0.05 qt dt grams hour X (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? ?=180000 The limiting amount does not grams depend on the amount that was present initially.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Transcribed Image Text:A pond initially contains 6,000,000 gal of water and an unknown
amount of an undesirable chemical.
Water containing 0.03 grams of this chemical per gallon flows into
the pond at a rate of 300 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).
dq
9-0.05 qt
dt
grams
hour
X
(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?
?=180000
The limiting amount does not
grams
depend on the amount that
was present initially.
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