$\"\"$

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(a).

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Find the concentration after $\"\"$ seconds, if the initial concentration is $\"\"$ .

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Consider $\"\"$ then the equation becomes $\"\"$ .

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Compare tha above equation with change in decay rate $\"\"$ .

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Here $\"\"$ .

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Rewrite the equation $\"\"$ .

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The only solution of the differential equation $\"\"$ are the exponential functions in the form of $\"\"$ .

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The solution of the diffential equation is $\"\"$ .

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The initial concentration is $\"\"$ , therefore $\"\"$ .

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

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$\"\"$

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$\"\"$

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

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$\"\"$

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Substitue $\"\"$ in the above equation.

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Expression for concentration is $\"\"$ .

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$\"\"$

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(b).

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Find the time to reduce $\"\"$ % of its original value.

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Expression for concentration is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ seconds.

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The time to reduce $\"\"$ % of its original value is $\"\"$ seconds.

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$\"\"$

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(a) Expression for concentration is $\"\"$ .

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(b). The time to reduce $\"\"$ % of its original value is $\"\"$ seconds.