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

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. 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. Rate of increase of total personal income: dollars.

Explanation / Answer

let population =p , percapitaincome =i ,total personal income=P

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

total personal income,P =p*i

differentiate with respect to t

product rule: dP/dt =((dp/dt)(i))+((p)(di/dt))

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

dP/dt =281455600+1345960000

dP/dt =1627415600

total personal income increases at 1627415600 dollars per year

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