$\"\"$

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Total population in Richmond area in $\"\"$ is $\"\"$ .

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Population was increasing by $\"\"$ per year.

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Average annual income in Richmond area in $\"\"$ is $\"\"$ .

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Rate of increase of average annual income $\"\"$ .

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Let total personal income in Richmond area as $\"\"$ .

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Let average annual income in Richmond area as $\"\"$ .

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Total personal income is the function $\"\"$ and $\"\"$ .

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Total personal income $\"\"$ .

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Differentiate with respect to $\"\"$ on each side.

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Product rule of derivatives: $\"\"$ .

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$\"\"$ .

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Here ,

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$\"\"$ Rate of increase of total personal income at time $\"\"$ .

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$\"\"$ Rate of increase of total population at time $\"\"$ .

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$\"\"$ Rate of increase of total population at time $\"\"$ .

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$\"\"$

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Find $\"\"$ in 1999.

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$\"\"$

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We have $\"\"$ and $\"\"$ .

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Substitute above values in $\"\"$

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$\"\"$

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$\"\"$

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Total personal income increase in $\"\"$ is $\"\"$

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Total personal income increase in Richmond area in $\"\"$ is $\"\"$ .

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