Question

in this exercise, we estimate the rate at which the total personal annual income was rising in the richmond - petersburg, virginia, metropolitan area in 1999. the total personal annual income is the sum of the annual incomes of all the people who live in that area.
in 1999, the population in this area was 961400, and the population was increasing at roughly 9200 people per year. the average annual income was 30593 dollars per capita, and this average was increasing at about 1400 dollars per year.
use the product rule and these figures to estimate the rate at which the total personal annual income rose in the richmond - petersburg area in 1999.
rate of increase of total personal annual income:
note: you are in the reduced scoring period: all work counts for 85% of the original.

Explanation:

Step1: Recall the Product Rule

The Product Rule states that if \(y = uv\), then \(y^\prime=u^\prime v + uv^\prime\). Let \(u\) be the population and \(v\) be the per - capita income.

Step2: Identify the values

We have \(u = 961400\), \(u^\prime=9200\), \(v = 30593\), \(v^\prime = 1400\)

Step3: Apply the Product Rule

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Answer:

\(1627415600\) dollars per year