Step by step
The question
Question: V = 20000 × (0.85)ᵗ is the value, in dollars, of a car t years after it is bought.
What does 20000 mean?
We write the equation big, so we can label it.
1 What the letters mean
V is the value of a car, in dollars.
t is the number of years.
It is the small raised number, the power: how many times we multiply by 0.85.
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 0.85 zero times.
That is why 0.85 to the power 0 is 1.
20000 times 1 is 20000.
t = 1: 0.85 to the power 1 is just 0.85.
20000 times 0.85 is 17000.
t = 2: 0.85 squared is 0.85 times 0.85.
20000 times 0.85 is 17000.
Times 0.85 again: 17000 times 0.85 is 14450.
Look at the values of V: 20000, 17000, 14450.
Each time t goes up 1, V is multiplied by 0.85.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
0.85 is what we multiply by, once for each year.
That is the power t: it counts the years.
20000 is V at t = 0: the first number in the table.
So 20000 is the value of a car at the start.
Careful!
20000 is not added each year.
It is the amount at t = 0, before any multiplying.
4 Say it in words
So 20000 means: the value of a car is 20000 dollars at t = 0.
That is the start.
5 Check
Let's check by going back one year, from t = 1 to t = 0.
To get to t = 1, we multiplied by 0.85.
To go back, we divide by 0.85.
17000 divided by 0.85 is 20000: the start.
It works!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: say it in words.
Last: check.