Estimate the rate at which the total personal income is rising in a metropolitan

Question

Estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 993,600, and the population was increasing at roughly 9900 people per year. The average annual income was $29,001 per capita, and this average was increasing at about $1400 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.

Please explain how you come to your answer. Thanks.

Explanation / Answer

percapita = total income / total population

so

total income(I) = percapita(C)* total population(P)

differencitation on both sidea using product rule.

dI/dt = P(dC/dt) + C(dP/dt)

dI = 993600*1400 + 29001*9900

dI = 1391040000 + 287109900

dI = 1678149900

rate of change of total personal income is $ 1678149900 per year.

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