Step by step
The question
Question: P = 800 × (1.1)ᵗ is the number of birds on an island t years from now.
What does 1.1 mean?
We write the equation big, so we can label it.
1 What the letters mean
P is the number of birds.
t is the number of years.
It is the small raised number, the power: how many times we multiply by 1.1.
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 1.1 zero times.
That is why 1.1 to the power 0 is 1.
800 times 1 is 800.
t = 1: 1.1 to the power 1 is just 1.1.
800 times 1.1 is 880.
t = 2: 1.1 squared is 1.1 times 1.1.
800 times 1.1 is 880.
Times 1.1 again: 880 times 1.1 is 968.
Look at the values of P: 800, 880, 968.
Each time t goes up 1, P is multiplied by 1.1.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
800 is P at t = 0: the first number in the table.
So 800 is the number of birds at the start.
1.1 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.
1.1 times 100 is 110.
So 1.1 is 110%.
110% is all of it, 100%, plus 10% more.
Careful!
110% is the new amount: the 100% it had, plus 10%.
The growth is only the part above 100%: 10%.
5 Say it in words
So 1.1 means: the number of birds goes up by 10% each year.
6 Check
Let's check the 10%.
10% is 10/100, that is 0.1.
10% of 800 is 0.1 times 800: 80.
800 plus 80 is 880: 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.