Physical Science B Semester Exam

21 of 3021 of 30 Items

Question
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

13 tacks
13 tacks

16 tacks
16 tacks

20 tacks
20 tacks
Skip to navigation

1 answer

To make a prediction for the number of tacks the electromagnet with 48 coils will pick up, we can look at the pattern in the data provided:

  • 12 coils pick up 4 tacks
  • 24 coils pick up 9 tacks
  • 36 coils pick up 13 tacks

Let's calculate the increase in the number of tacks for the increase in coils:

  1. From 12 to 24 coils (12 more coils), the number of tacks increased from 4 to 9 (an increase of 5 tacks).
  2. From 24 to 36 coils (another 12 more coils), the number of tacks increased from 9 to 13 (an increase of 4 tacks).

Observing these increases:

  • The first 12 coils yielded 5 tacks (around 0.42 tacks per coil).
  • The next 12 coils yielded 4 tacks (around 0.33 tacks per coil).

There seems to be a diminishing return for each additional coil. If we assume this trend continues, we can predict the next increase in tacks for going from 36 to 48 coils (which is an increase of 12 coils).

If we consider previous increases and assume a continued slight decrease in the number of tacks per coil gained, we might add around 3 tacks for the additional 12 coils since the trend indicates a reduction:

  • 36 coils = 13 tacks
  • Predicted for 48 coils = 13 tacks + 3 tacks = 16 tacks

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