Question

Town A and Town B both currently have a population of 10, 000 people. If Town A increases by 500 people a year and Town B increases by 10% each year, when will the two towns have the same population again?

Answer 1

Let:

ya = Total population of town A

yb = Total population of town B

ya and yb are given by:

`\begin{gathered} ya=10000+500x \\ yb=10000(1.1)^x \end{gathered}`

We need to know when:

ya = yb

`\begin{gathered} 10000+500x=10000(1.1)^x \\ \end{gathered}`

Solve for x:

`\begin{gathered} x=0 \\ 10000=10000 \end{gathered}`

The only real solution is x = 0

Therefore, the towns will never have the same population again after the year 0