A tank initially contains a solution of 6 pounds of salt in 40 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 9 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) = 0077 Submit Question

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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A tank initially contains a solution of 6 pounds of salt in 40 gallons of water. Water with 1/2 pound of salt
per gallon is added to the tank at 9 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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Transcribed Image Text:A tank initially contains a solution of 6 pounds of salt in 40 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 9 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→∞ Submit Question
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