To solve for the number of tacks the electromagnet with 48 coils will pick up, we can analyze the pattern in the provided results:
- 12 coils → 4 tacks
- 24 coils → 9 tacks
- 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.