Step by step
The question
Question: V = 3000 × (0.8)ᵗ is the value, in dollars, of a computer t years after it is bought.
What does 0.8 mean?
We write the equation big, so we can label it.
1 What the letters mean
V is the value of a computer, in dollars.
t is the number of years.
It is the small raised number, the power: how many times we multiply by 0.8.
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 0.8 zero times.
That is why 0.8 to the power 0 is 1.
3000 times 1 is 3000.
t = 1: 0.8 to the power 1 is just 0.8.
3000 times 0.8 is 2400.
t = 2: 0.8 squared is 0.8 times 0.8.
3000 times 0.8 is 2400.
Times 0.8 again: 2400 times 0.8 is 1920.
Look at the values of V: 3000, 2400, 1920.
Each time t goes up 1, V is multiplied by 0.8.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
3000 is V at t = 0: the first number in the table.
So 3000 is the value of a computer at the start.
0.8 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.
0.8 times 100 is 80.
So 0.8 is 80%.
80% is what is left.
100% take away 80% is 20%: the part that is lost.
Careful!
80% is the part that is left.
The part that is lost is 20%.
5 Say it in words
So 0.8 means: the value of a computer goes down by 20% each year.
6 Check
Let's check the 20%.
20% is 20/100, that is 0.2.
20% of 3000 is 0.2 times 3000: 600.
3000 minus 600 is 2400: 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.