Step by step
The question
Question: P = 2500 × (1.04)ᵗ is the number of people in a town t years from now.
What does 1.04 mean?
We write the equation big, so we can label it.
1 What the letters mean
P is the number of people.
t is the number of years.
It is the small raised number, the power: how many times we multiply by 1.04.
2 Make a small table
To see what each number does, we try a few years: 0, 1 and 2.
0 is where it starts.
t = 0: no years have passed, so we multiply by 1.04 zero times.
That is why 1.04 to the power 0 is 1.
2500 times 1 is 2500.
t = 1: 1.04 to the power 1 is just 1.04.
2500 times 1.04 is 2600.
t = 2: 1.04 squared is 1.04 times 1.04.
2500 times 1.04 is 2600.
Times 1.04 again: 2600 times 1.04 is 2704.
Look at the values of P: 2500, 2600, 2704.
Each time t goes up 1, P is multiplied by 1.04.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
2500 is P at t = 0: the first number in the table.
So 2500 is the number of people at the start.
1.04 is what we multiply by, once for each year.
That is the power t: it counts the years.
4 Write it as a percent
A percent is out of 100: one whole is 100%.
So we multiply by 100.
1.04 times 100 is 104.
So 1.04 is 104%.
104% is all of it, 100%, plus 4% more.
Careful!
104% is the new amount: the 100% it had, plus 4%.
The growth is only the part above 100%: 4%.
5 Say it in words
So 1.04 means: the number of people goes up by 4% each year.
6 Check
Let's check the 4%.
4% is 4/100, that is 0.04.
4% of 2500 is 0.04 times 2500: 100.
2500 plus 100 is 2600: the same as the table at t = 1.
It works!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: write it as a percent.
Then: say it in words.
Last: check.