Question

I suck at story problems! can i please get some help?

on january 1st, 2010, chessville has a population of 50,000 people. Chessville then enters a period of population growth. it's population increases 7% each year. On the same day, Checkersville has a population of 70,000 people. Checkersville starts to experience a population decline. Its population decreases 4% each year. During what year will the population of Chessville first exceed that of Checkersville? show all your work and explain your steps.

Answer 1

Chessville starts at 50,000 people, and each year the population increases by 7%. If \(C_0 = 50,000\) then the population of Chessville, \[P_C = C_0*(1 + 7/100)^n\] where \(n\) is the number of years that have passed since January 1, 2010. We could also write \[P_C = C_0*(1+7/100)^{(y-2010)}\] for a slightly snazzier formula where \(y\) is the actual year.

Checkersville will have a similar formula, except there the initial value will be 70,000, and the quantity inside the parentheses will be (1 - 4/100) to reflect the decreasing population.

Set the two of them to be equal, then remember your log properties to solve for y. That will get you the year in which the curves intersect.

Does that make sense? Try to solve it, and show your work if you get stuck.

Answer 2

thanks! it makes sense :)

Answer 3

Great! By the way, if you want a good book (IMO) on story problems, go to your library or bookstore and look for "How to Solve Word Problems in Algebra" by Mildred Johnson. She does a nice job of going through all the usual kinds of problems and showing you how to set them up systematically.

Answer 4

alright! i will look into that :)