Students build four electromagnets and test them by picking up metal tacks. Here are their partial results.

12 coils 4 tacks
24 9 tacks
36 coils 13 tacks
48 coils ?tacks
Whih is the best prediction for the number of nails the electromagnet with 48 coils will pick up?
A: 20 tacks B: 16 tacks C: 13 tacks D:12 tacks

1 answer

To predict the number of tacks that an electromagnet with 48 coils will pick up, we can analyze the data provided.

Let's look at the relationship between the number of coils and the number of tacks picked up:

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

We can see that as the number of coils increases, the number of tacks picked up also increases. Let's calculate the increase in tacks per additional set of coils:

  1. From 12 coils to 24 coils (12 coils increase):

    • 9 tacks - 4 tacks = 5 tacks (for 12 coils)
    • Increase per coil = 5 tacks / 12 coils = 0.4167 tacks per coil
  2. From 24 coils to 36 coils (12 coils increase):

    • 13 tacks - 9 tacks = 4 tacks (for 12 coils)
    • Increase per coil = 4 tacks / 12 coils = 0.3333 tacks per coil

The increase in tacks has decreased as we added more coils, implying diminishing returns as coils are increased.

To estimate the increase for 48 coils:

Continuing this trend, the next change from 36 coils to 48 coils is again 12 coils. Assuming the average tacks per coil is around the previous averages, we can guess a slightly diminished rate of increase.

A rough estimate could be:

  • From 36 coils (13 tacks), if we assume an increase of about 4 tacks for the next 12 coils (which is slightly less than what we got from the previous intervals), we get:

\[ 13 tacks + 4 tacks = 17 tacks \]

Since none of the options above have 17, we need to select the closest available option. The options given are:

A: 20 tacks, B: 16 tacks, C: 13 tacks, D: 12 tacks

The best option for the number of tacks that the electromagnet with 48 coils will pick up is:

B: 16 tacks

This choice is the closest estimate based on the observed pattern.