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 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.)

Explanation / Answer

total personnal income TI=populatipn n* percapita income i

TI=n*i

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

differentiate with respect to time t

dTI/dt =(dn/dt)i+ n(di/dt)

given n=987300, dn/dt =10000, i=29001,di/dt=1300

dTI/dt =(10000*29001)+ (987300*1300)

dTI/dt =1573500000

total personnel income rising at 1573500000$ per year

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