To fill in the missing parts of the table, we need to establish a pattern or relationship between the values of \( x \) (number of days) and \( y \) (number of texts).
Given the current values:
- When \( x = 0 \), \( y = c \)
- When \( x = 7 \), \( y = d \)
- When \( x = b \), \( y = 300 \)
Assuming a linear relationship between \( x \) and \( y \), we can try to find a pattern based on the provided numbers.
Known Values
- \( x = 1 \) corresponds to \( y = 75 \),
- \( x = 7 \) corresponds to \( y = d \),
- \( x = b \) corresponds to \( y = 300 \).
Let's take the increment between \( x = 0 \) and \( x = 7 \):
- Assume \( 0 \) corresponds to texts \( c \).
- For \( x = 7 \) (after 7 days), \( y = d \).
Linear Assumption
Let’s say the change in text messages per day is constant:
- If \( y \) increases from \( c \) at \( x = 0 \) to \( d \) at \( x = 7 \):
Let’s develop a formula that concerns \( 300 \) and will use that to find values \( a \) and \( b \).
Finding Values
- First, we have \( 0 \) to \( 75 \) ( \( y = 75 \) when \( x = 1 \)).
- We can assume an increasing trend. Hence let’s sketch the table:
| x - # of days | 0 | 1 | 7 | b | |---------------|---|----|---|---| | y - # of texts | c | 75 | d | 300 |
From 1 to 7, if \( c = 75 \):
- texts increase from \( 75 \) to \( d \).
- Let’s estimate \( d \approx 150 \) (arbitrary guess that occurs with doubling).
Then we can set, \( b = 14 \) leading to \( y \) increase consistently, aiming for \( 300 \).
Filling-in Table
Assuming a doubling pattern:
- \( c = 0 \)
- \( a = 1 \)
- \( d = 150 \)
- \( b = 14 \)
So we can finalize the table as follows:
| x - # of days | 0 | 1 | 7 | 14 | |---------------|----|----|-----|-----| | y - # of texts | 0 | 75 | 150 | 300 |
Thus, the table with missing parts filled will look like this:
| x - # of days | 0 | 1 | 7 | 14 | |---------------|---|----|-----|-----| | y - # of texts | 0 | 75 | 150 | 300 |
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