Step by step
The question
Question: A town has 12000 people and grows 2.5% each year.
How many people after 4 years?
1 Find the start and the factor
The start is 12000.
Each year it keeps all of it, 100%, and gets 2.5% more.
So it becomes 102.5% of what it was.
102.5% is 102.5/100: 1.025.
That is the factor.
2 Write the rule
x is the number of years.
Each year we multiply by 1.025 again.
So y = 12000 × 1.025ˣ.
Careful!
The 2.5% is taken of the NEW amount every year, not always of 12000.
3 Put in x = 4
After 4 years, x = 4.
1.025 to the power 4 is 1.103813.
So we multiply 12000 by 1.103813.
That is 13245.754687, about 13246.
4 Check
Let's check year by year.
We start at 12000, and multiply by 1.025 each year.
After 4 years we get 13245.754687 again.
It works!
Let's look back.
First: find the start and the factor.
Then: write the rule.
Then: put in x = 4.
Last: check.