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

20 tacks
20 tacks

16 tacks
16 tacks

13 tacks
13 tacks

12 tacks

1 answer

To solve for the number of tacks the electromagnet with 48 coils will pick up, we can analyze the pattern in the provided results:

  1. 12 coils → 4 tacks
  2. 24 coils → 9 tacks
  3. 36 coils → 13 tacks

Let's look at the increase in the number of tacks as the number of coils increases:

  • From 12 to 24 coils (12 coils increase), the number of tacks increases from 4 to 9 (5 tacks increase).
  • From 24 to 36 coils (12 coils increase), the number of tacks increases from 9 to 13 (4 tacks increase).

Now we can summarize these increases:

  • (12 coils → 9 tacks): 5 tacks over 12 coils
  • (24 coils → 13 tacks): 4 tacks over 12 coils

The increase in tacks starts at 5 and then decreases to 4 as the coil number increases. Assuming a similar trend continues, we can estimate the increase for 48 coils.

From 36 to 48 coils (an additional 12 coils), we might expect a further decrease in the rate of increase, potentially going below 4 tacks.

If we extrapolate that the increase might be around 4 or slightly less, we can estimate:

  • If we assume an increase of about 4 tacks, from 13 (number of tacks at 36 coils), we can predict:
    • 13 + 4 = 17 tacks (but this is a conservative estimate)

Given this trend, the closest response option is 16 tacks, as it suggests a decrease in the rate of increase.

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