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 2500 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.
1.04 is what we multiply by, once for each year.
That is the power t: it counts the years.
2500 is P at t = 0: the first number in the table.
So 2500 is the number of people at the start.
Careful!
2500 is not added each year.
It is the amount at t = 0, before any multiplying.
4 Say it in words
So 2500 means: the number of people is 2500 at t = 0.
That is the start.
5 Check
Let's check by going back one year, from t = 1 to t = 0.
To get to t = 1, we multiplied by 1.04.
To go back, we divide by 1.04.
2600 divided by 1.04 is 2500: the start.
It works!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: say it in words.
Last: check.