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 954,300, and the population was increasing at roughly 9800 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. (Round your answer to three decimal places.)
$--------------------- billion per year

Answer 1

P- Population function

I - Income function

P₁₉₉₉ = 954300

d/dt(P) = 9800

I_{1999 =} 29001

d/dt(I) = 140

Rate of increase of total personal income = d/dt(P * I)

d/dt(P * I) = P* d/dt(I) + I*d/dt (P)

= 954300*1400 + 29001*9800

= 1,336,020,000 + 284,209800

= 1,620,229,800

Rate of increase of total personal income is $,620,229,800 per year