Question

19.
Write a function rule for the table.

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

Answer 1

To determine the function rule for the given table of days and cost to rent a truck, let's analyze the data points:

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

We notice that as the number of days increases, the cost increases as well. Let's calculate the change in cost for each increase in day:

- From 1 day to 2 days: \(56 - 34 = 22\)
- From 2 days to 3 days: \(78 - 56 = 22\)
- From 3 days to 4 days: \(100 - 78 = 22\)

The cost increases by $22 for each additional day. This indicates a linear relationship.

Now, we can define the equation for the cost (C) in terms of the number of days (D). The relationship can be expressed in the form:

\[ C = mD + b \]

Where:
- \(m\) is the slope (the cost increase per day)
- \(b\) is the y-intercept (the initial cost when \(D = 0\))

From the data, we see that:
- The slope \(m = 22\).

We need to determine the y-intercept. To find \(b\), we can use one of the provided points. Let's use \(D = 1\) and \(C = 34\):

\[ 34 = 22(1) + b \]
\[ 34 = 22 + b \]
\[ b = 34 - 22 \]
\[ b = 12 \]

So, the function rule that describes the cost to rent a truck based on the number of days is:

\[ C = 22D + 12 \]

This means that the cost to rent a truck increases by $22 for each day, starting from an initial cost of $12.