A town of 5000 people grows by 10% a year. How many people live…

Step by step

The question

Question: A town of 5000 people grows by 10% a year.

How many people live there after 2 years?

1 Find the start and the factor

The start is 5000.

Each year it keeps all of it, 100%, and gets 10% more.

So it becomes 110% of what it was.

110% is 1.1.

That is the factor.

2 Write the rule

x is the number of years.

Each year we multiply by 1.1 again.

So y = 5000 × 1.1ˣ.

Careful!

The 10% is taken of the NEW amount every year, not always of 5000.

3 Put in x = 2

After 2 years, x = 2.

1.1 to the power 2 is 1.21.

So we multiply 5000 by 1.21.

So it is 6050.

4 Check

Let's check year by year.

We start at 5000, and multiply by 1.1 each year.

After 2 years we get 6050 again.

It works!

Let's look back.

First: find the start and the factor.

Then: write the rule.

Then: put in x = 2.

Last: check.