Linear or exponential: x 0, 1, 2, 3; y 2, 3, 5, 9

Step by step

The question

Question: is this table linear or exponential: x is 0, 1, 2, 3, and y is 2, 3, 5, 9?

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 1, then plus 2, then plus 4.

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.

3/2 is 1.5.

5/3 is about 1.67.

9/5 is 1.8.

The ratios are not the same either.

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

3 Check

Let's check: the changes 1, 2, 4 are not all the same, and the ratios are not all the same.

So neither is right!

Let's look back.

First: check the differences.

Then: check the ratios.

Last: check.