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

by illjazz
Tags: estimating, income, personal, rate, rising, town
 P: 59 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!
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 Quote by illjazz 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!
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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