A tank initially contains a solution of 7 pounds of salt in 60 gallons of water. Water with 3/10 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q'(t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t) = t→∞

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A tank initially contains a solution of 7 pounds of salt in 60 gallons of water. Water with 3/10 pound of salt per
gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote
the quantity (lbs) of salt at time t (min).
(a) Write a differential equation for Q(t).
Q'(t) =
(b) Find the quantity Q(t) of salt in the tank at time t > 0.
(c) Compute the limit.
lim Q(t) =
t→∞
Transcribed Image Text:A tank initially contains a solution of 7 pounds of salt in 60 gallons of water. Water with 3/10 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q'(t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t) = t→∞
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