Step by step
The question
Question: A = 2000 × (1.03)ᵗ is the money in a savings account, in dollars, t years from now.
What does 2000 mean?
We write the equation big, so we can label it.
1 What the letters mean
A is the money, in dollars.
t is the number of years.
It is the small raised number, the power: how many times we multiply by 1.03.
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 1.03 zero times.
That is why 1.03 to the power 0 is 1.
2000 times 1 is 2000.
t = 1: 1.03 to the power 1 is just 1.03.
2000 times 1.03 is 2060.
t = 2: 1.03 squared is 1.03 times 1.03.
2000 times 1.03 is 2060.
Times 1.03 again: 2060 times 1.03 is 2121.8.
Look at the values of A: 2000, 2060, 2121.8.
Each time t goes up 1, A is multiplied by 1.03.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
1.03 is what we multiply by, once for each year.
That is the power t: it counts the years.
2000 is A at t = 0: the first number in the table.
So 2000 is the money at the start.
Careful!
2000 is not added each year.
It is the amount at t = 0, before any multiplying.
4 Say it in words
So 2000 means: the money is 2000 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 1.03.
To go back, we divide by 1.03.
2060 divided by 1.03 is 2000: 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.