A colony of 3000 ants grows by 50% a month. How many ants are there…

Step by step

The question

Question: A colony of 3000 ants grows by 50% a month.

How many ants are there after 3 months?

1 Find the start and the factor

The start is 3000.

Each month it keeps all of it, 100%, and gets 50% more.

So it becomes 150% of what it was.

150% is 1.5.

That is the factor.

2 Write the rule

x is the number of months.

Each month we multiply by 1.5 again.

So y = 3000 × 1.5ˣ.

Careful!

The 50% is taken of the NEW amount every month, not always of 3000.

3 Put in x = 3

After 3 months, x = 3.

1.5 to the power 3 is 3.375.

So we multiply 3000 by 3.375.

So it is 10125.

4 Check

Let's check month by month.

We start at 3000, and multiply by 1.5 each month.

After 3 months we get 10125 again.

It works!

Let's look back.

First: find the start and the factor.

Then: write the rule.

Then: put in x = 3.

Last: check.