Step by step
The question
Question: A = 400 × (0.95)ᵗ is the number of animals in a forest t years from now.
What does 0.95 mean?
We write the equation big, so we can label it.
1 What the letters mean
A is the number of animals.
t is the number of years.
It is the small raised number, the power: how many times we multiply by 0.95.
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 0.95 zero times.
That is why 0.95 to the power 0 is 1.
400 times 1 is 400.
t = 1: 0.95 to the power 1 is just 0.95.
400 times 0.95 is 380.
t = 2: 0.95 squared is 0.95 times 0.95.
400 times 0.95 is 380.
Times 0.95 again: 380 times 0.95 is 361.
Look at the values of A: 400, 380, 361.
Each time t goes up 1, A is multiplied by 0.95.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
400 is A at t = 0: the first number in the table.
So 400 is the number of animals at the start.
0.95 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.
0.95 times 100 is 95.
So 0.95 is 95%.
95% is what is left.
100% take away 95% is 5%: the part that is lost.
Careful!
95% is the part that is left.
The part that is lost is 5%.
5 Say it in words
So 0.95 means: the number of animals goes down by 5% each year.
6 Check
Let's check the 5%.
5% is 5/100, that is 0.05.
5% of 400 is 0.05 times 400: 20.
400 minus 20 is 380: 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.