Question

Write a function rule for the table.

Days Cost to Rent a Truck
1 29
2 47
3 65
4 83








c = 18d + 18


c = 18d


c = 18d + 11


c = 11d + 18

Answer 1

To understand the relationship between the number of days (d) and the cost to rent a truck (c), we can look at the values in the table:

- For 1 day: Cost is $29
- For 2 days: Cost is $47
- For 3 days: Cost is $65
- For 4 days: Cost is $83

Let's find the cost increase per day:

- From day 1 to day 2: 47 - 29 = 18
- From day 2 to day 3: 65 - 47 = 18
- From day 3 to day 4: 83 - 65 = 18

This indicates that the cost increases by $18 for each additional day of rental.

Now, let's determine a function rule. We can observe that for \(d = 1\), \(c\) is $29.

We can express the cost formula in terms of \(d\):

1. The cost increase is 18 per day.
2. The initial cost when renting for 1 day is $29.

So the function rule can be derived as follows:

- The recurring cost from the additional days can be represented as \(c = 18d\) (which alone doesn’t account for the base cost).
- However, we need to add the initial amount we get when renting for the first day: to represent the total cost starting from \(d = 1\), we can adjust the equation.

For \(1\) day (which corresponds to \(d=1\)):
\[ c = 18(1) + 11 = 29 \]

We can generalise this as follows:
\[ c = 18d + 11 \]

So, the correct function rule is:

\[ c = 18d + 11 \]

This matches the values in the table:

- For \(d = 1\): \(c = 18(1) + 11 = 29\)
- For \(d = 2\): \(c = 18(2) + 11 = 47\)
- For \(d = 3\): \(c = 18(3) + 11 = 65\)
- For \(d = 4\): \(c = 18(4) + 11 = 83\)

Thus, the correct answer is:

**c = 18d + 11**.