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Problem. A tank initially contains 100 gallons of brine solution with concentration 2 pound of salts per gallon. Beginning at time zero, brine containing 1 pound of salt per gallon is being added to the tank at the rate of 2 gallons per minute, and the mixture is being poured out of the tank at the rate of 3 gallons per minute. Find a general function indicating the amount of salt in the tank in terms of time t. (a) Set up an initial value problem describing the amount A(t) of salts in the tank at any time. (b) Solve the initial value problem in Part (a). (c) Find the amount of salts in the tank when there are 50 gallons of brine left in the tank.

Problem. A tank initially contains 100 gallons of brine solution with concentration 2 pound of salts per gallon. Beginning at time zero, brine containing 1 pound of salt per gallon is being added to the tank at the rate of 2 gallons per minute, and the mixture is being poured out of the tank at the rate of 3 gallons per minute. Find a general function indicating the amount of salt in the tank in terms of time t. (a) Set up an initial value problem describing the amount A(t) of salts in the tank at any time. (b) Solve the initial value problem in Part (a). (c) Find the amount of salts in the tank when there are 50 gallons of brine left in the tank.

Algebra & Trigonometry with Analytic Geometry
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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Problem. A tank initially contains 100 gallons of brine solution with concentration 2 pound of salts per gallon. Beginning at time zero, brine containing 1 pound of salt per gallon is being added to the tank at the rate of 2 gallons per minute, and the mixture is being poured out of the tank at the rate of 3 gallons per minute. Find a general function indicating the amount of salt in the tank in terms of time t. (a) Set up an initial value problem describing the amount A(t) of salts in the tank at any time. (b) Solve the initial value problem in Part (a). (c) Find the amount of salts in the tank when there are 50 gallons of brine left in the tank.
Transcribed Image Text:Problem. A tank initially contains 100 gallons of brine solution with concentration 2 pound of salts per gallon. Beginning at time zero, brine containing 1 pound of salt per gallon is being added to the tank at the rate of 2 gallons per minute, and the mixture is being poured out of the tank at the rate of 3 gallons per minute. Find a general function indicating the amount of salt in the tank in terms of time t. (a) Set up an initial value problem describing the amount A(t) of salts in the tank at any time. (b) Solve the initial value problem in Part (a). (c) Find the amount of salts in the tank when there are 50 gallons of brine left in the tank.
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