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

11 paperclips
11 paperclips

1 paperclip
1 paperclip

14 paperclips
14 paperclips

8 paperclips

1 answer

To predict the number of paperclips the electromagnet with 30 coils will pick up, let's analyze the data provided for the electromagnets and the number of paperclips they picked up:

  • 8 coils -> 2 paperclips
  • 16 coils -> 7 paperclips
  • 24 coils -> 11 paperclips

Now, we can see the relationship between the number of coils and the number of paperclips:

  • From 8 to 16 coils, the number of paperclips increases from 2 to 7 (an increase of 5 paperclips).
  • From 16 to 24 coils, the number of paperclips increases from 7 to 11 (an increase of 4 paperclips).

Looking at the pattern, let's analyze how much the number of paperclips increases with additional coils. The differences in paperclips per added coils don't follow a fixed pattern, but it seems to range around 4 to 5 paperclips for every increase of 8 coils.

Continuing this pattern from 24 coils to 30 coils, we can see that adding 6 coils (the difference from 24 to 30) might lead to an increase of around 2 to 3 paperclips.

If we assume that with 30 coils, the number of paperclips increases by about 3, we would project:

11 (current number with 24 coils) + 3 = 14 paperclips.

Thus, the best prediction for the number of paperclips the electromagnet with 30 coils will pick up is:

14 paperclips.