$\"\"$

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(a)

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statement : The rate of change of $\"\"$ with respect to $\"\"$ is proportional to $\"\"$ .

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$\"\"$ is proportional to $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Apply integral on each side.

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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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$\"\"$

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(b)

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The direction field satisfies $\"\"$ along $\"\"$ .

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The differential equation matches with the slope field $\"\"$ .

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$\"\"$

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(c)

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Verification :

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Graph the differential equation $\"\"$ .

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Graph :

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$\"\"$

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Observe the graph :

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The differential equation matches with the slope field $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) The differential equation matches with the slope field $\"\"$ .

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(c) Graph:

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$\"\"$

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The differential equation matches with the slope field $\"\"$ .