Explanation Given: Amount of brine solution in tanks A and B is 100 gallons. And, amount of salt in tank A is represented by x 1 ( t ) and amount of salt in tank B is represented by x 2 ( t ) . Calculation: The integral for a function of form f ( x ) = x m is given by, ∫ f ( x ) d x = x m + 1 m + 1 Consider tank A , the amount of water entering the tank is, 7 + 1 = 8 gallon/min And the amount of water leaving the tank is, − 5 − 3 = − 8 gallon/min Therefore, there is no change in the amount of water in tank A . So, the equation for concentration of salt in tank A is, x 1 ( t ) 100 lb gallon Consider tank B , the amount of water entering the tank is 8 gallon/min . And the amount of water leaving the tank is, − 4 − 1 = − 5 gallon/min Therefore, there is no change in the amount of water in tank B . So, the equation for concentration of salt in tank B is, x 2 ( t ) 100 lb gallon If the total amount of water is leaving the tank, then the rate of flow of water will be taken as negative and if the total amount of water is entering the tank, then the rate of flow will be taken as positive for both tanks A and B Multiply the rate at which water is entering and leaving the tank with concentration of salt for each tank

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

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Chapter 2, Problem 44CR

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To describe: A mathematical model for the number of pounds of salt in tanks A and B.

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Chapter 2, Problem 43CR

Chapter 2, Problem 45CR

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A mathematical model for the number of pounds of salt in tanks A and B .

Solution Summary: The author describes the mathematical model for the number of pounds of salt in tanks A and B at any time.

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To describe: A mathematical model for the number of pounds of salt in tanks A and B.

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Chapter 2 Solutions