Step by step
The question
Question: U = 1500 × (1.2)ᵗ is the number of app users t months from now.
What does 1.2 mean?
We write the equation big, so we can label it.
1 What the letters mean
U is the number of app users.
t is the number of months.
It is the small raised number, the power: how many times we multiply by 1.2.
2 Make a small table
To see what each number does, we try a few months: 0, 1 and 2.
0 is where it starts.
t = 0: no months have passed, so we multiply by 1.2 zero times.
That is why 1.2 to the power 0 is 1.
1500 times 1 is 1500.
t = 1: 1.2 to the power 1 is just 1.2.
1500 times 1.2 is 1800.
t = 2: 1.2 squared is 1.2 times 1.2.
1500 times 1.2 is 1800.
Times 1.2 again: 1800 times 1.2 is 2160.
Look at the values of U: 1500, 1800, 2160.
Each time t goes up 1, U is multiplied by 1.2.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
1500 is U at t = 0: the first number in the table.
So 1500 is the number of app users at the start.
1.2 is what we multiply by, once for each month.
That is the power t: it counts the months.
4 Write it as a percent
A percent is out of 100: one whole is 100%.
So we multiply by 100.
1.2 times 100 is 120.
So 1.2 is 120%.
120% is all of it, 100%, plus 20% more.
Careful!
120% is the new amount: the 100% it had, plus 20%.
The growth is only the part above 100%: 20%.
5 Say it in words
So 1.2 means: the number of app users goes up by 20% each month.
6 Check
Let's check the 20%.
20% is 20/100, that is 0.2.
20% of 1500 is 0.2 times 1500: 300.
1500 plus 300 is 1800: 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.