The populations of two towns are changing at steady rates. One town has a population of 25,500. It's population is increasing by 2000 people each year. The other town has a population of 47,900. It's population is decreasing by 800 people each year. If the rates for each town remain the same in how ma ny years will the populations be the same?
2006-11-23 11:16:28 · 4 answers · asked by curiousgeorge2 2 in Science & Mathematics ➔ Mathematics
List out the population of each town?
Town A: 25,500; 27,500; 29,500; 31,500; 33,500; 35,500; 37,500; 39,500; 41,500; 43,500; 45,500; 47,500...
Town B: 47,900; 47,100; 46,300; 45,500; 44,700; 43,900; 43,100; 42,300; 41,500; 40,700...
You'll notice that after 8 years, you'll end up with 41,500 people per town.
But modulo_function has a good method for solving though. I'd never thought of using 2 straight lines and finding their intersection to solve your question.
Hope this helps :)
2006-11-23 11:45:22 · answer #1 · answered by chyrellos 2 · 0⤊ 0⤋
In 8 years with a population of 41,500 people.
2006-11-23 19:31:24 · answer #2 · answered by sara M 2 · 0⤊ 0⤋
1st town = 25,500, increasing 2000 each year
2nd town = 47,900, decreasing 800 each year
x = years it takes for them to equal
25,500 + 2000x = 47,900 - 800x --- Add 800 x to each side...
2800x + 25,500 = 47,900 --- Subtract 25,500 from both sides...
2800x = 22,400 --- Divide both sides by 2800...
x = 8
It will take 8 years for their populations to be the same.
2006-11-23 19:46:49 · answer #3 · answered by Anonymous · 0⤊ 0⤋
You do recognize that you're looking for the intersection of two lines, don't you?
"steady rates" means constant slopes, that's the big clue. At t=0, start time, you know values of p(t), these are the vertical intercepts.
p1 = s1*t + 25,500
p2 = s2*t + 47,900
don't forget that s2 is negative...
2006-11-23 19:27:42 · answer #4 · answered by modulo_function 7 · 1⤊ 0⤋