Let:
ya = Total population of town A
yb = Total population of town B
ya and yb are given by:
[tex]\begin{gathered} ya=10000+500x \\ yb=10000(1.1)^x \end{gathered}[/tex]We need to know when:
ya = yb
[tex]\begin{gathered} 10000+500x=10000(1.1)^x \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} x=0 \\ 10000=10000 \end{gathered}[/tex]The only real solution is x = 0
Therefore, the towns will never have the same population again after the year 0
