Question

What equation models the data in the table if d = number of days and c = cost?


Days Cost
2 44
3 66
5 110
6 132








c = 22d


c = d + 22

Answer 1

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.

1. **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.

2. **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:

**\( c = 22d \)**.