In this exercise, we estimate the rate at which the total personal income is rising in the Richmond-Petersburg, Virginia, metropolitan 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.

The question is incomplete The complete question is

Estimate the rate at which the total personal income is rising. The population is 961,400 and it increases by 9,200 people per year. The average annual income is 30,593 dollars per capita, and this increases by 1,400 dollars per year.  Using the product rule, estimate the rate at which the total personal income rises.

The answer is 3.58%

Step-by-step explanation:

The population of the area = 961,400

Population increase at the rate of 9,200 per year

Average annual income = $30,593

Average annual income increase rate at $1400 per year.

The total annual income will be calculated as population of the area times the average annual income

$961,400 X $30,593 = $29,412,110,200

The expected annual income increase for the entire population will be calculated as average annual income increase times entire population

$1,400 X 961,400 =  $1,345,960,000

 Then the annual income after increase will be a summation of average total annual income and the expected annual increase in income

$29,412,110,200 + $1,345,960,000 =$30,758,070,200

To get the total population after increase, we add the total population to the rate of increase of the population

961,400 + 9,200 =970,600

To get the expected average annual income after increase we divide the total annual income after increase by the total population after increase  

$30,758,070,200 / 970,600 =$31,689.75

Finally, to get the total annual income increase for the entire population, we divide the average annual income increase by the average annual income

$31,689.75/$30,593.00=1.0358 - 1 =.0358 X 100 =3.58%

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