To find the function rule that describes the relationship between the number of days (d) and the cost to rent a truck (c), we can analyze the values given in the table:
- For 1 day, cost = 34
- For 2 days, cost = 57
- For 3 days, cost = 80
- For 4 days, cost = 103
We can observe the pattern in how the cost increases as the number of days increases:
- From day 1 to day 2: \( 57 - 34 = 23 \)
- From day 2 to day 3: \( 80 - 57 = 23 \)
- From day 3 to day 4: \( 103 - 80 = 23 \)
The cost increases by $23 for each additional day of rental. This indicates a linear relationship.
To find the cost formula, we need to find the base cost when d = 0. To do this, we can set \( d = 0 \) in our linear equation and solve for the y-intercept (which will give us the base cost).
Since the cost for 1 day is $34, and the cost increases by $23 for each additional day, we can think of it as:
\[ c = 23d + C_0 \]
where \( C_0 \) is the initial base cost when \( d = 0 \).
To find \( C_0 \), we can set \( d = 1 \):
\[ c = 23(1) + C_0 = 34 \]
This means:
\[ 23 + C_0 = 34 \]
Subtracting 23 from both sides gives:
\[ C_0 = 34 - 23 = 11 \]
Thus the cost formula can be expressed as:
\[ c = 23d + 11 \]
So the correct rule is:
\( c = 23d + 11 \)
This corresponds to the last option provided.