SOLUTION: In 2000, the population of Charleston, South Carolina, was 116,300. During the 1990s, its population increased at an average rate of 800 people per year. In 2000, the population of

Algebra ->  Systems-of-equations -> SOLUTION: In 2000, the population of Charleston, South Carolina, was 116,300. During the 1990s, its population increased at an average rate of 800 people per year. In 2000, the population of      Log On


   

Question 1040263: In 2000, the population of Charleston, South Carolina, was 116,300. During the 1990s, its population increased at an average rate of 800 people per year. In 2000, the population of Greenville, South Carolina, was 56,002. During the 1990s, its population decreased at an average rate of 228 per year. Suppose the population of each city continues to increase and decrease, respectively, at these rates. Approximately how many years ago (from the year 2000) would the populations of the two cities have been the same?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For each city, plot +p+, population on the
vertical axis and p / n
Rate for Greenville, SC: +-228+ p / n
------------------------------------
Equation for Charleston, SC:
+p+=+116300+%2B+800n+
Equation for Greenville, SC:
+p+=+56002+-+228n+
-----------------------
Set the 2 populations equal to each other
+116300+%2B+800n+=+56002+-+228n+
+1028n+=+56002+-+116300+
+1028n+=+-60298+
+n+=+-58.656+
In 1941, ( 59 years before 2000 ), the cities populations
would have been the same
--------------------------
check:
+p+=+116300+%2B+800%2A%28+-58.656+%29+
+p+=+116300+-+46924.8+
+p+=+69375.2+
and
+p+=+56002+-+228%2A%28+-58.656+%29+
+p+=+56002+%2B+13373.568+
+p+=+69375.568+
I think that's close enough
Here's the plots:
( year 2000 is at +n+=+0+ )