Question

Estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 918,000, and the population was increasing at roughly 9700 people per year. The average annual income was $34,549 per capita, and this average was increasing at about $1300 per year (a little above the national average of about $1225 yearly).
Required:
Use the Product Rule to estimate the rate at which total personal income was rising in the area in 1999.

Answer 1

Answer:

$X=\ 1.64*10^9$

Step-by-step explanation:

From the question we are told that:

Population size $P=918000$

Rate of Population increase  $\frac{dP}{dt}=9700$

Average annual income $I= \ 34,549$

Rate of annual income increase  $\frac{dI}{dt}=\ 1300$

Generally the equation for Total Income is mathematically given by

$X=P \frac{dI}{dt}+I \frac{dP}{dt}$

$X=918000*1400+(9200*30593)$

$X=\ 1.64*10^9$