Word problems (product rule of derivatives)

[reneeg]

I am having trouble knowing where to start with this problem. A step by step solution would be appreciated as I have 5 similar questions within my assignment.

The population of a country Dnalge is 50 million in 1997 and increasing at a rate of 0.8 million per year. The average annual income of a person in Dnalge during 1997 was 18000 dollars per year and increasing at a rate of 900 dollars per year.
How quickly was the total income of the entire population rising in 1997?
______ dollars per year

(At this point I am familiar with most derivate rules up to - but not including - the quotient rule, as well as determining maximas and minimas.)

 

[stapel]

The population of a country Dnalge is 50 million in 1997 and increasing at a rate of 0.8 million per year. The average annual income of a person in Dnalge during 1997 was 18000 dollars per year and increasing at a rate of 900 dollars per year. How quickly was the total income of the entire population rising in 1997?

Using what you learned back in algebra, create an expression for the growth of the population.

. . . . .year 0: 50 + 0
. . . . .year 1: 50 + 1(0.8)
. . . . .year 2: 50 + 2(0.8)
. . . . .year 3: 50 + 3(0.8)

...and so forth, until you see the pattern. Then create the expression for "year x". Do the same thing for the growth of the per-capita income.

The total income is of course the product of the population and the per-capita income, so multiply to create the function for the total income.

To find the change in total income, apply the Product Rule.

If you get stuck, please reply showing all of your work and reasoning. Thank you!

Eliz.