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

  1. Jul 23, 2008 #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. Jul 23, 2008 #2


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    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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