In this exercise, we estimate the rate at which the total personal income is ris

Question

In this exercise, we estimate the rate at which the total personal income is rising in the Richmond-Petersburg, Virginia, metropolitan area. In 1999, the population in this area was 961400, and the population was increasing at roughly 9200 people per year. The average annual income was 30593 dollars per capita, and this average was increasing at about 1400 dollars per year [a little above the national average of about 1225 dollars yearly] .

Use the Product Rule and these figures to estimate the rate at which the total personal income was rising in the Richmond-Petersburg area in 1999.

Explanation / Answer

total personal income P=population p *percapitaincome i

P=p*i

the population in this area was 961400, and the population was increasing at roughly 9200 people per year. The average annual income was 30593 dollars per capita, and this average was increasing at about 1400 dollars per year

given p=961400, dp/dt=9200, i=30593,di/dt=1400

P=pi

differentiate with respect to time

product rule:(uv)'=u'v+uv'

dP/dt =(dp/dt)i +p(di/dt)

dP/dt =((9200)(30593)) +((961400)(1400))

dP/dt =((9200)(30593)) +((961400)(1400))

dP/dt=1627415600

total personal income is rising at 1627415600 $ per year

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