To determine the equation that models the data in the table, we can analyze the relationship between the number of days (d) and the cost (c).
Let's look at the given data points:
- For \(d = 2\), \(c = 16\)
- For \(d = 3\), \(c = 24\)
- For \(d = 5\), \(c = 40\)
- For \(d = 6\), \(c = 48\)
Now we can look at how \(c\) changes with respect to \(d\):
- When \(d = 2\), \(c = 16 = 8 \times 2\)
- When \(d = 3\), \(c = 24 = 8 \times 3\)
- When \(d = 5\), \(c = 40 = 8 \times 5\)
- When \(d = 6\), \(c = 48 = 8 \times 6\)
From this, we can observe that the cost \(c\) is equal to \(8\) times the number of days \(d\).
Thus, the equation that models the data is:
\[ c = 8d \]
This matches the first option you provided.