Question

We estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 918,100, and the population was increasing at roughly 9300 people per year. The average annual income was $29,001 per capita, and this average was increasing at about $1400 per year (a little above the national average of about $1225 yearly). Use the Product Rule and these figures to estimate the rate at which total personal income was rising in the area in 1999. (Round your answer to three decimal places.)

Answer 1

the rate at which total personal income was rising in the area in 1999 is 1.5550493×10⁹

Explanation:

Given that:

the population of this area P was 918,100

and the population was increasing at roughly 9300 people per year i.e DP/DT = 9300

The average annual income I was $29,001 per capita

and this average was increasing at about $1400 per year

i.e DI/DT = 1400

Using the Produle rule;

the rate at which total personal income was rising in the area in 1999 can be calculate as:

DC/DT = P(DI/DT)+I(DP/DT)

DC/DT = 918100(1400)+29001(9300)

DC/DT = 1.28534×10⁹ + 269709300

DC/DT = 1.5550493×10⁹

Thus; the rate at which total personal income was rising in the area in 1999 is 1.5550493×10⁹