# In this exercise, we estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 987,300, and the population was increasing at...

In this exercise, we estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 987,300, and the population was increasing at roughly 10000 people per year. The average annual income was $29,001 per capita, and this average was increasing at about $1300 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.)

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### 1 Answer

In 1999, the population of the metropolitan area was 987300 and it was increasing at roughly 10000 people per year. The average annual income was $29001 per capita, and this average was increasing at about $1300 per year.

The total personal income is equal to the product of the per capita personal income and the total population. Initially this is equal to 987300*29001. This increases to (987300+10000)*(29001+1300).

The difference of the two values is the increase in the total personal income and is equal to 987300*1300+10000*29001+10000*1300.

The rate of increase is 987300*1300+10000*29001+10000*1300 divided by 987300*29001

This is approximately equal to 0.05540 or 5.540%

**The rate of increase in the total personal income is 5.540%**