Question

1. the table shows the total number y of rolls of wrapping paper sold by a student after x weeks.

x	1	2	3	4	5	6
y	3	5	9	12	17	24

Explanation:

Since the problem is not fully presented (e.g., what is being asked about the table, like finding a function, slope, or something else), we can't provide a complete solution. But if we assume a common problem like finding the type of sequence or the equation of the line (though the differences here are not constant: 5 - 3 = 2, 9 - 5 = 4, 12 - 9 = 3, 17 - 12 = 5, 24 - 17 = 7, so it's not linear, maybe quadratic or another type), we need more details.

If you want to find, for example, the differences or the pattern, here's a start:

Step1: Calculate first differences

Find \( y_{n + 1}-y_n \) for consecutive \( x \):
For \( x = 1 \) to \( x = 2 \): \( 5 - 3 = 2 \)
For \( x = 2 \) to \( x = 3 \): \( 9 - 5 = 4 \)
For \( x = 3 \) to \( x = 4 \): \( 12 - 9 = 3 \)
For \( x = 4 \) to \( x = 5 \): \( 17 - 12 = 5 \)
For \( x = 5 \) to \( x = 6 \): \( 24 - 17 = 7 \)

Step2: Calculate second differences (if needed)

Find differences of the first differences:
\( 4 - 2 = 2 \), \( 3 - 4=- 1 \), \( 5 - 3 = 2 \), \( 7 - 5 = 2 \)
(The second differences are not constant, so maybe a different approach like looking for a quadratic or other function)

But without the actual question, we can't proceed further. Please provide the full question (e.g., "Find the equation of the line of best fit", "Determine if the sequence is linear", "Predict the number of rolls sold after 7 weeks", etc.) to get a complete solution.

Answer:

Step1: Calculate first differences

Find \( y_{n + 1}-y_n \) for consecutive \( x \):
For \( x = 1 \) to \( x = 2 \): \( 5 - 3 = 2 \)
For \( x = 2 \) to \( x = 3 \): \( 9 - 5 = 4 \)
For \( x = 3 \) to \( x = 4 \): \( 12 - 9 = 3 \)
For \( x = 4 \) to \( x = 5 \): \( 17 - 12 = 5 \)
For \( x = 5 \) to \( x = 6 \): \( 24 - 17 = 7 \)

Step2: Calculate second differences (if needed)

Find differences of the first differences:
\( 4 - 2 = 2 \), \( 3 - 4=- 1 \), \( 5 - 3 = 2 \), \( 7 - 5 = 2 \)
(The second differences are not constant, so maybe a different approach like looking for a quadratic or other function)

But without the actual question, we can't proceed further. Please provide the full question (e.g., "Find the equation of the line of best fit", "Determine if the sequence is linear", "Predict the number of rolls sold after 7 weeks", etc.) to get a complete solution.