Estimating the rate at which the total personal income of a town is rising

  1. 1. The problem statement, all variables and given/known data
    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 of this area was 961,400, and the population was increasing at roughly 9200 people per year. The average annual income was $30,593 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 Richmond-Petersburg area in 1999. Explain the meaning of each term in the Product Rule.


    2. Relevant equations
    Product Rule: (fg)' = fg' + gf'


    3. The attempt at a solution
    I haven't gotten very far at all. I've taken all the figures given and written them out into a table, like so:

    year: 1999
    population: 961,400
    population growth: 9200 people/year
    avg. annual income per capita: $30,593
    avg. income growth: $1400/year
    national avg. income growth: $1225/year

    So that's what's given. I'm told I need to use the Power Rule, which I understand. What I do not understand is where to begin. I tried to see what f(x) and g(x) will be here but can't wrap my head around it.

    Pointers would be appreciated. Thanks!
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,946
    Staff Emeritus
    Science Advisor

    Who told you you need to use a power rule? I don't see any application of it here. As you say, the product rule is (fg)'= f'g+ fg'. You are given population and population growth rate and you are given average income and its growth rate. Total income is population*average income. The obvious thing to do is take f= population, g= average income. Of course, f' and g' then are the growth rates.
     
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