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 963,200, and the population was increasing at roughly 9300 people per year. The average annual income was $33,162 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.)

Question

Shayna Sampson

Mathematics

28 January, 07:16

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 963,200, and the population was increasing at roughly 9300 people per year. The average annual income was $33,162 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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Answers (1)

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Arely Nicholson · Answer 1

4.923%

Step-by-step explanation:

Population in 1999

963,200

Average annual income

$33,162 per capita

Total personal income

963,200 * 33,162 = $31,941,638,400

Population in 2000

963,200+9,300 = 972,500

Average annual income

$33,162 + $1,300 = $34,462 per capita

Total personal income

972,500 * 34,462 = $33,514,295,000

We must now find a number x such that 31,941,638,400 increased x% equals 33,514,295,000. That is to say,

31,941,638,400 * (1+x/100) = 33,514,295,000

Isolating x we have

x = 4.923%

And the rate at which total personal income was rising in the area in 1999 was 4.923%