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 [a little above the national average of about 1225 dollars yearly] .

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.

Answer 1

help please i really don't understand how do do this

Answer 2

let p(t) be the population so
p(t) = 961400 + 9200(t-1999)
let c(t) be the income per capita so
c(t) = 30593 + 1400(t-1999)

so we want (if i understand the question)
d(p(t)c(t)) / dt at point t= 1999
since the total income is p(t) * c(t)

Answer 3

are you there ? agree? can you do it now ?

Answer 4

no not really

Answer 5

d(p(t)c(t)) / dt = product rule = dp(t)/dt * c(t) + p(t) * d(c(t))/dt
= 9200 * [ 30593 + 1400(t-1999) ] + [961400 + 9200(t-1999)]*1400
at point t=1999 we get
9200 * 30593 + 961400*1400

Answer 6

thanks for explain how you got your answer

Answer 7

yw