$\"\"$

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Let $\"\"$ be the number of pounds of concentrate in the solution at any time $\"\"$ .

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The number of gallons of solution in the tank at any time $\"\"$ is $\"\"$ .

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The tank loses $\"\"$ gallons of solution per minute.

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Therefore, the tank lose concentrate at the rate is $\"\"$ .

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The solution gains concentrate at the rate $\"\"$ .

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Thereforem, the net rate of change is $\"\"$ .

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(a)

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The equation is in the form of $\"\"$ .

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The differential equation is a first order linear differential equation.

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Solution of the first order linear differential equation is $\"\"$ is $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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The solution of differential equation is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$

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(b) Find the time at which the amount of concentrate in the tank reaches $\"\"$ .

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The amount of concentrate in the tank reaches $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

\

$\"\"$ .

\

$\"\"$

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(c) Find the quantity of concentrate in the solution as $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .

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(c) $\"\"$ .