Question

In 1996, Town M had a population of 30,500 people, and it has grown at a rate of 2% every year. In 1996, Town N had 32,500 people and the population has increased by a contrast rate of 600 people each year. In what year were the populations of the two towns approximately equal?

Answer 1

Forget the 1996 for the moment.  Just count the number of years that go by.

30500*(1.02)^x= 32500 + 600x The easiest way to handle this is either to use a spreadsheet or graph if. I don't see an algebraic way of doing it. I'll try the graph first.

The red line is y = 32500 + 600x

Now let's try a spreadsheet.

I can't copy and past a spreadsheet's contents, but it shows that they are about equal when x = 17.
y = 32500 + 600x gives 42700 when x = 17
y = 30500*(1.02)^17 gives 42707 when x = 17 You cannot get much closer than that.