CHANGING POPULATIONS

Highland has a population of $12,200$. Its population has been increasing at a rate of $300$ people per year. Lowville has a population of $21,000$ but is declining by $250$ people per year. Assuming these rates do not change, in how many years will the populations be equal?  

1. Write an equation that represents each city's population over time. What do your variables represent?

   Hint (a):

   How do the current populations and rates of change relate to $y = mx + b$?

   Hint (a):

   The rate of change is the slope.

   Answers (a):

   Highland: $y = 300x + 12,100$
   Lowville: $y = −250x + 21,000$

   Be sure to identify what the variable represent.

2. Solve the problem. Show your work.

   Hint (b):

   Use the Equal Values Method.