Calc word question?

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 900,700, and the population was increasing at roughly 9500 per year. The average annual income was $31,775 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.

Answer 1

total personal income = population * income per person

for "income per person" you use the average income given. Lets rename these variables to make the equation
T = P*I
Now differentiate both sides with respect to time:
dT/dt = I*dP/dt + P*dI/dt
dT/dt = (31775)*(9500) + (900700)*(1400)
dT/dt = 301862500 + 1260980000
dT/dt = 1562842500 total income/year

I hope that helps.