Explanation The rate at which the brine solution is pumped into the tank A is faster than the rate at which the solution is being pumped out. Therefore, the difference I the rate of inward flow and outward flow of solution is, R i n − R o u t = 3 − 2 R i n − R o u t = 1 gal/min For tank A , the net rate of x 1 ( t ) is, d x 1 d t = ( 3 ) ( x 2 100 − t ) − ( 2 ) ( x 1 100 + t ) d x 1 d t = 3 x 2 100 − t − 2 x 1 100 + t Thus, net rate of change for tank A is, d x 1 d t = 3 x 2 100 − t − 2 x 1 100 + t (1) For tank B , the net rate of x 2 ( t ) is, d x 2 d t = ( 2 ) ( To determine (b) Find A mathematical model for relationship between x 1 ( t ) and x 2 ( t ) that holds at time t and the amount of salt in tank at a given interval of time.

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.9, Problem 9E

To determine

(a)

Find a mathematical model for the number of pounds of salt at a given interval of time in both tanks A and B.

To determine

(b)

Find A mathematical model for relationship between x1(t) and x2(t) that holds at time t and the amount of salt in tank at a given interval of time.

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Chapter 2.9, Problem 8E

Chapter 2.9, Problem 10E

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(a) Find a mathematical model for the number of pounds of salt at a given interval of time in both tanks A and B .

Solution Summary: The author explains the mathematical model for the number of pounds of salt at a given interval of time in both tanks A and B.

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(a)

Find a mathematical model for the number of pounds of salt at a given interval of time in both tanks A and B.

(b)

Find A mathematical model for relationship between x1(t) and x2(t) that holds at time t and the amount of salt in tank at a given interval of time.

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Chapter 2 Solutions

(a) Find a mathematical model for the number of pounds of salt at a given interval of time in both tanks A and B .

Solution Summary: The author explains the mathematical model for the number of pounds of salt at a given interval of time in both tanks A and B.

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(a) Find a mathematical model for the number of pounds of salt at a given interval of time in both tanks A and B.

(b) Find A mathematical model for relationship between x1(t) and x2(t) that holds at time t and the amount of salt in tank at a given interval of time.

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Chapter 2 Solutions

(a)

Find a mathematical model for the number of pounds of salt at a given interval of time in both tanks A and B.

(b)

Find A mathematical model for relationship between x1(t) and x2(t) that holds at time t and the amount of salt in tank at a given interval of time.