To determine which equation models the data given in the table, let's analyze the data:
| Days (d) | Cost (c) | |----------|----------| | 2 | 44 | | 3 | 66 | | 5 | 110 | | 6 | 132 |
First, we'll check each equation.
- Equation 1: \( c = 22d \)
Using this equation, we can calculate the cost for each day:
- For \( d = 2 \):
\( c = 22 \times 2 = 44 \) - For \( d = 3 \):
\( c = 22 \times 3 = 66 \) - For \( d = 5 \):
\( c = 22 \times 5 = 110 \) - For \( d = 6 \):
\( c = 22 \times 6 = 132 \)
This equation matches all the data points in the table.
- Equation 2: \( c = d + 22 \)
Now, let's test this equation:
- For \( d = 2 \):
\( c = 2 + 22 = 24 \) - For \( d = 3 \):
\( c = 3 + 22 = 25 \) - For \( d = 5 \):
\( c = 5 + 22 = 27 \) - For \( d = 6 \):
\( c = 6 + 22 = 28 \)
This equation does not match the costs in the table at all.
Based on the analysis, the correct equation that models the data in the table is:
\( c = 22d \).