Step by step
The question
Question: P = 10000 × (1.025)ᵗ is the number of people in a city t years from now.
What does 1.025 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 1.025.
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 1.025 zero times.
That is why 1.025 to the power 0 is 1.
10000 times 1 is 10000.
t = 1: 1.025 to the power 1 is just 1.025.
10000 times 1.025 is 10250.
t = 2: 1.025 squared is 1.025 times 1.025.
10000 times 1.025 is 10250.
Times 1.025 again: 10250 times 1.025 is 10506.25.
Look at the values of P: 10000, 10250, 10506.25.
Each time t goes up 1, P is multiplied by 1.025.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
10000 is P at t = 0: the first number in the table.
So 10000 is the number of people at the start.
1.025 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.
1.025 times 100 is 102.5.
So 1.025 is 102.5%.
102.5% is all of it, 100%, plus 2.5% more.
Careful!
102.5% is the new amount: the 100% it had, plus 2.5%.
The growth is only the part above 100%: 2.5%.
5 Say it in words
So 1.025 means: the number of people goes up by 2.5% each year.
6 Check
Let's check the 2.5%.
2.5% is 2.5/100, that is 0.025.
2.5% of 10000 is 0.025 times 10000: 250.
10000 plus 250 is 10250: 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.