Linear or exponential: x 1, 2, 3, 4; y 1, 4, 9, 16

Step by step

The question

Question: is this table linear or exponential: x is 1, 2, 3, 4, and y is 1, 4, 9, 16?

We write it as a table.

x goes up by 1 each time.

1 Check the differences

Linear means: the same number is added each time.

So we look at the change from one y to the next: plus 3, then plus 5, then plus 7.

The changes are not the same.

So it is not linear.

2 Check the ratios

Exponential means: we multiply by the same number each time.

So we divide each y by the one before.

4/1 is 4.

9/4 is 2.25.

16/9 is about 1.78.

The ratios are not the same either.

So the table is neither: not linear and not exponential.

3 Check

Let's check: the changes 3, 5, 7 are not all the same, and the ratios are not all the same.

In fact, y is x squared: a curve, but not exponential.

So neither is right!

Let's look back.

First: check the differences.

Then: check the ratios.

Last: check.