Scatterplot (0, 100) (1, 52) (2, 24) (3, 13) (4, 6): linear or… Step by Step

Step by step

The question

Question: does a linear or an exponential model fit this scatterplot better?

linear or exponential?

1 Look at the points

Each dot is one point of the data: across is x, up is y.

x goes up by 1 each time, the same step.

So we can compare each point with the one before.

x: 0, 1, 2, 3, 4 same step: + 1

We write the points in a table.

2 Check the differences

Linear means: about the same number is added each step.

So we look at the change from one y to the next: minus 48, then minus 28, then minus 11, then minus 7.

The changes are getting smaller and smaller.

They are not about the same.

So it is not linear.

= − 48, − 28, − 11, − 7: not the same

Careful!

Going down each step does not make it linear.

Linear needs about the same number added every step.

Careful: it goes down each step, but that is not linear

3 Check the ratios

Exponential means: we multiply by about the same number each step.

So we divide each y by the one before.

52/100 is about 0.52.

24/52 is about 0.46.

13/24 is about 0.54.

6/13 is about 0.46.

= 52100 ≈ 0.52, 2452 ≈ 0.46, 1324 ≈ 0.54, 613 ≈ 0.46

All close to 0.5.

y is multiplied by about 0.5 each step.

So an exponential model fits better.

= about × 0.5 every step → exponential

4 Check

Let's check on the picture.

A straight line from the first point to the last one misses the points in the middle.

A curve that multiplies by about 0.5 each step goes through the points, or very close.

So the exponential model is right!

the curve passes close to every point; the line does not

Let's look back.

First: look at the points.

Then: check the differences.

Then: check the ratios.

Last: check.

Answer