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:
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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.
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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