To find a function rule that relates the number of days (\(d\)) to the cost to rent a truck (\(c\)), we can analyze the data given in the table:
- For Day 1: Cost is $34
- For Day 2: Cost is $56
- For Day 3: Cost is $78
- For Day 4: Cost is $100
From the observations, we can see that the cost increases by $22 for each additional day:
- From Day 1 to Day 2: \(56 - 34 = 22\)
- From Day 2 to Day 3: \(78 - 56 = 22\)
- From Day 3 to Day 4: \(100 - 78 = 22\)
This indicates that the cost increases linearly with the number of days.
To express this as a function, we can identify the following:
- For \(d = 1\), \(c = 34\).
- The change in cost per day (\(m\)) is $22.
The general form of a linear equation is:
\[ c = md + b \]
Where:
- \(m\) is the slope (change of cost per day),
- \(b\) is the y-intercept.
From the table, we know that when \(d = 0\) (not listed), \(c\) would be the cost released from the base value (the minimum value when no days are rented).
If we plug in the known variables, we can find \(b\): By using any known point. Let's use \(d = 1\) and \(c = 34\):
\[ 34 = 22(1) + b \implies b = 34 - 22 = 12 \]
Thus, we can write the function rule as:
\[ c = 22d + 12 \]
This matches the first option you provided.
To summarize, the function rule that describes the cost to rent a truck as a function of days rented is:
\[ c = 22d + 12 \]