Question

Write a function rule for the table.

Days Cost to Rent a Truck
1 34
2 56
3 78
4 100








c = 22d + 22


c = 22d


c = 12d + 22


c = 22d + 12

Answer 1

To determine the function rule based on the table provided, we can analyze the cost to rent a truck for different numbers of days.

**Days and Costs:**
- 1 day: $34
- 2 days: $56
- 3 days: $78
- 4 days: $100

**Finding the Pattern:**

1. **Calculate the Increase in Cost per Day:**
- From 1 to 2 days: 56 - 34 = 22
- From 2 to 3 days: 78 - 56 = 22
- From 3 to 4 days: 100 - 78 = 22

The increase in cost for each additional day is consistently $22.

2. **Finding the Base Cost:**
- We can see that for 1 day of rental, the cost is $34. This suggests that the cost may be a function of the number of days \(d\) plus some initial (base) cost.

The linear relationship can be expressed as:
\[ c = \text{(Cost per day)} \times d + \text{Base cost} \]

Where:
- Cost per day = $22
- Initial cost (base cost when days = 0) can be determined by observing the cost when \(d = 1\).

**Let’s express the function:**
To find the total cost \(c\), we establish:
\[ c = 22d + 12 \]

This matches all provided values:
- For \(d = 1\): \(c = 22(1) + 12 = 22 + 12 = 34\)
- For \(d = 2\): \(c = 22(2) + 12 = 44 + 12 = 56\)
- For \(d = 3\): \(c = 22(3) + 12 = 66 + 12 = 78\)
- For \(d = 4\): \(c = 22(4) + 12 = 88 + 12 = 100\)

Thus, the correct rule for the cost to rent a truck based on days is:
\[ c = 22d + 12 \]

So, the answer is:
**c = 22d + 12**