Question

14.
Write a function rule for the table.

Days Cost to Rent a Truck
1 34
2 50
3 66
4 82

Answer 1

To derive a function rule for the relationship between the number of days and the cost to rent a truck, we first need to analyze the data given in the table:

| Days | Cost to Rent a Truck |
|------|----------------------|
| 1 | 34 |
| 2 | 50 |
| 3 | 66 |
| 4 | 82 |

Next, we can observe how the cost changes as the number of days increases.

1. Calculate the difference in cost for consecutive days:
- From Day 1 to Day 2: \(50 - 34 = 16\)
- From Day 2 to Day 3: \(66 - 50 = 16\)
- From Day 3 to Day 4: \(82 - 66 = 16\)

The cost increases by 16 dollars for each additional day of rental. This indicates a linear relationship.

2. The cost for renting a truck appears to start at $34 for 1 day, which is a constant (the y-intercept).

Since the cost increases by $16 for each additional day, we can say the slope (rate of increase, m) is 16. Therefore, we can formulate the cost as:

\[
\text{Cost} = m \times \text{Days} + b
\]

Where:
- \(m\) (slope) = 16 (cost per day)
- \(b\) (y-intercept) = 34 (base cost for the first day)

Thus, we can express the function rule as:

\[
\text{Cost} = 16 \times \text{Days} + 18
\]

However, if we rewrite it considering that the start of the Days is 1 rather than 0, the corrected function can be structured as:

\[
\text{Cost} = 16 \times (\text{Days} - 1) + 34
\]
or simplified to focus on Days starting from 1:

\[
\text{Cost} = 16 \times \text{Days} + 18
\]

This correctly gives you the cost based on the number of days you rent the truck.