To fill in the missing parts of the table, we need to establish a relationship between the number of days (x) and the number of texts (y).
We have two given data points:
- When x = 0, y = c (we need to find c).
- When x = 7, y = d (we need to find d).
- When x = b, y = 300 (we need to find b).
We can try to find a pattern with the given points. We know the following:
- For x = 0, y = c
- For x = a, y = 75
- For x = 7, y = d
- For x = b, y = 300
Now, we can analyze the given options (0, 2, 3, 5, 10, 12, 13, 50, 75, 175) to see if we can find correspondences.
Let's assume that as the number of days increases, the number of texts also increases. A logical assumption can be that every subsequent entry corresponds to an increase in the number of texts.
If we set:
- c = 0 (when x = 0),
- a = 5 (makes sense as a middle point between 0 and 7; shows growth),
- d = 175 (a reasonable increase from 75 with an increase to 300 when we assume several texts were sent),
- b = 10 (fits the increase pattern up to 300).
The changes in the number of texts may seem linear or could have an exponential growth nature on certain intervals.
The completed table would read:
| x - # of days | 0 | 5 | 7 | 10 | |---------------|---|----|----|----| | y - # of texts | 0 | 75 | 175| 300|
So, the values would be: a = 5, b = 10, c = 0, d = 175.
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