1. A tank initially holds 10 gal of fresh water. At t = 0, a brine solution containing 1/2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, while the well-stirred mixture leaves the tank at the same rate. Find (a) the amount and (b) the concentration of salt in the tank at any time t.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. A tank initially holds 10 gal of fresh water. At t =
0, a brine solution containing 1/2 lb of salt per
gallon is poured into the tank at a rate of 2 gal/min,
while the well-stirred mixture leaves the tank at the
same rate. Find (a) the amount and (b) the
concentration of salt in the tank at any time t.
2. A tank initially holds 80 gal of a brine solution
containing 1/8 lb of salt per gallon. At t = 0,
another brine solution containing 1 lb of salt per
gallon is poured into the tank at the rate of 4
gal/min, while the well-stirred mixture leaves the
tank at the rate of 8 gal/min. Find the amount of
salt in the tank when the tank contains exactly 40
gal of solution.
3. A tank contains 100 gal of brine made by
dissolving 80 lb of salt in water. Pure water runs
into the tank at the rate of 4 gal/min, and the well-
stirred mixture runs out at the same rate. Find (a)
the amount of salt in the tank at any time t and (b)
the time required for half the salt to leave the tank.
Transcribed Image Text:1. A tank initially holds 10 gal of fresh water. At t = 0, a brine solution containing 1/2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, while the well-stirred mixture leaves the tank at the same rate. Find (a) the amount and (b) the concentration of salt in the tank at any time t. 2. A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t = 0, another brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 8 gal/min. Find the amount of salt in the tank when the tank contains exactly 40 gal of solution. 3. A tank contains 100 gal of brine made by dissolving 80 lb of salt in water. Pure water runs into the tank at the rate of 4 gal/min, and the well- stirred mixture runs out at the same rate. Find (a) the amount of salt in the tank at any time t and (b) the time required for half the salt to leave the tank.
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