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.

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okpalawalter8 okpalawalter8 · Answer 1 · 2021-07-23T04:33:09+02:00

Answer:

[tex]X=\$1.64*10^9[/tex]

Step-by-step explanation:

From the question we are told that:

Population size [tex]P=918000[/tex]

Rate of Population increase [tex]\frac{dP}{dt}=9700[/tex]

Average annual income [tex]I= \$34,549[/tex]

Rate of annual income increase [tex]\frac{dI}{dt}=\$1300[/tex]

Generally the equation for Total Income is mathematically given by

[tex]X=P \frac{dI}{dt}+I \frac{dP}{dt}[/tex]

[tex]X=918000*1400+(9200*30593)[/tex]

[tex]X=\$1.64*10^9[/tex]