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.
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