Samuel builds four electromagnets and tests them by picking up paperclips. Here are his partial results.

Coils

Paperclips

8 2
16 7
24 11
30 ?

Which is the best prediction for the number of paperclips the electromagnet with 30 coils will pick up?

(1 point)
Responses

14 paperclips
14 paperclips

11 paperclips
11 paperclips

8 paperclips
8 paperclips

1 paperclip

1 answer

To make a prediction about the number of paperclips that the electromagnet with 30 coils will pick up, we can observe the pattern in the data provided:

  • For 8 coils, the electromagnet picks up 2 paperclips.
  • For 16 coils, it picks up 7 paperclips.
  • For 24 coils, it picks up 11 paperclips.

Let's calculate the increase in the number of paperclips per additional coils:

  • From 8 to 16 coils (8 coils): 7 - 2 = 5 paperclips
  • From 16 to 24 coils (8 coils): 11 - 7 = 4 paperclips

We can see that the number of paperclips increases by fewer each time as the number of coils increases.

Now, let’s find the average increase to predict what would happen with 30 coils:

  • The increase from 8 to 16 coils is 5 paperclips for 8 coils.
  • The increase from 16 to 24 coils is 4 paperclips for 8 coils.

The increases seem to be declining by around 1 paperclip for each subsequent increase of 8 coils.

Now, let's estimate the increase from 24 coils to 30 coils, which is another increase of 6 coils (not 8), but we can use a similar pattern:

  • If we continue the pattern, the increase might be around 3 to 4 paperclips for this increase (assuming a continued decrease).

If we add approximately 3 paperclips to the 11 paperclips yielded at 24 coils, we get:

11 paperclips + 3 paperclips = 14 paperclips.

Therefore, the best prediction for the number of paperclips the electromagnet with 30 coils will pick up is 14 paperclips.