Question

Estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 918,000, and the population was increasing at roughly 9700 people per year. The average annual income was $34,549 per capita, and this average was increasing at about $1300 per year (a little above the national average of about $1225 yearly).

Required:
Use the Product Rule to estimate the rate at which total personal income was rising in the area in 1999.

Answer 1

`X=\$1.64*10^9`

Explanation:

From the question we are told that:

Population size
`P=918000`

Rate of Population increase
`(dP)/(dt)=9700`

Average annual income
`I= \$34,549`

Rate of annual income increase
`(dI)/(dt)=\$1300`

Generally the equation for Total Income is mathematically given by

`X=P (dI)/(dt)+I (dP)/(dt)`

`X=918000*1400+(9200*30593)`

`X=\$1.64*10^9`