The current population of Watertown is 951,200, and the population is increasing

Question

The current population of Watertown is 951,200, and the population is increasing by roughly 9,200 people per year. The current average annual income is $30,600 per capita, and this average is increasing by roughly $1400 per year. Given that the total personal income of Watertown is the product of the population size and the average income, use the product rule to estimate the rate at which the total personal income rises.

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The current population of Watertown is 951,200, and the population is increasing by roughly 9,200 people per year. The current average annual income is $30,600 per capita, and this average is increasing by roughly $1400 per year. Given that the total personal income of Watertown is the product of the population size and the average income, use the product rule to estimate the rate at which the total personal income rises.

Explanation / Answer

Change in product (xy) = x*change in y + y*change in x + change in x* change in y

Thus, change in total personal income = population* change in per capita income + per capita income*change in population + change in percapita income* change in population
= 951200*1400 + 30600* 9200 + 1400*9200 = 1,331,680,000+281,520,000 + 12,880,000 = 1,626,080,0000
Thus the total personal income is rising by 1626.08 $ million per year
or at the rate of 1.62608 $billion per year

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