Students build four electromagnets and test them by picking up metal tacks. Here are their partial results. 12 coils 4 tacks 24 coils 9 tacks 36 coils 13 tacks 48 coils ? tacks Which is the best prediction for the number of nails the electromagnet with 48 coils will pick up?(1 point) Responses 12 tacks 12 tacks 16 tacks 16 tacks 13 tacks 13 tacks 20 tacks

1 answer

To predict the number of tacks the electromagnet with 48 coils will pick up, we can analyze the given data to find a pattern or trend in the relationship between the number of coils and the number of tacks picked up.

Here are the results provided:

  • 12 coils → 4 tacks
  • 24 coils → 9 tacks
  • 36 coils → 13 tacks
  • 48 coils → ? tacks

Next, let's look for a pattern in the increase of the number of tacks per increase of coils:

  1. From 12 coils to 24 coils (increase of 12 coils): 4 tacks to 9 tacks (increase of 5 tacks)
  2. From 24 coils to 36 coils (increase of 12 coils): 9 tacks to 13 tacks (increase of 4 tacks)
  3. From 36 coils to 48 coils (increase of 12 coils): The pattern seems to show a decreasing return on increase in number of tacks.

To estimate the number of tacks at 48 coils, we notice that the increment in tacks is reducing (from 5 to 4). The last increment (9 to 13) is +4 tacks. If we follow the trend of reducing increments, we can expect the next increment (from 13) to be smaller than 4.

A reasonable estimate can be assuming an increment of about 3 tacks at 48 coils:

13 tacks + 3 tacks = 16 tacks.

Thus, the best prediction for the number of tacks the electromagnet with 48 coils will pick up is 16 tacks.