Question
Write a function rule for the table.
Days Cost to Rent a Truck
1 34
2 57
3 80
4 103
c = 23d
c = 23d + 11
c = 11d + 23
c = 23d + 23
Days Cost to Rent a Truck
1 34
2 57
3 80
4 103
c = 23d
c = 23d + 11
c = 11d + 23
c = 23d + 23
Answers
GPT-4o mini
To find the function rule for the relationship between the number of days (d) and the cost (c) to rent a truck based on the table provided, we can look for a linear relationship in the data.
The given data is as follows:
- For 1 day (d = 1), the cost (c) is $34.
- For 2 days (d = 2), the cost (c) is $57.
- For 3 days (d = 3), the cost (c) is $80.
- For 4 days (d = 4), the cost (c) is $103.
### Step 1: Determine the cost per day
To find the cost per day, we can determine the increase in cost as the number of days increases:
- The increase from day 1 to day 2: \( 57 - 34 = 23 \)
- The increase from day 2 to day 3: \( 80 - 57 = 23 \)
- The increase from day 3 to day 4: \( 103 - 80 = 23 \)
The cost increases by $23 for each additional day.
### Step 2: Formulate the function rule
Given that the increase per day is $23, we can express the total cost as:
- Initial cost for the first day: $34
- Additional cost for each additional day: \( 23d \)
However, we need to find the correct relationship that includes a fixed initial cost. It appears that $34 corresponds to the cost when renting for 1 day, which suggests we can derive the formula as follows:
The correct formula can be inferred as:
\[ c = 23d + 11 \]
### Step 3: Check the formula with the given values
1. For \( d = 1 \):
\[ c = 23(1) + 11 = 23 + 11 = 34 \]
2. For \( d = 2 \):
\[ c = 23(2) + 11 = 46 + 11 = 57 \]
3. For \( d = 3 \):
\[ c = 23(3) + 11 = 69 + 11 = 80 \]
4. For \( d = 4 \):
\[ c = 23(4) + 11 = 92 + 11 = 103 \]
All values match the cost given in the table.
### Conclusion
The function rule that represents the cost to rent a truck based on the number of days is:
\[ \boxed{c = 23d + 11} \]
The given data is as follows:
- For 1 day (d = 1), the cost (c) is $34.
- For 2 days (d = 2), the cost (c) is $57.
- For 3 days (d = 3), the cost (c) is $80.
- For 4 days (d = 4), the cost (c) is $103.
### Step 1: Determine the cost per day
To find the cost per day, we can determine the increase in cost as the number of days increases:
- The increase from day 1 to day 2: \( 57 - 34 = 23 \)
- The increase from day 2 to day 3: \( 80 - 57 = 23 \)
- The increase from day 3 to day 4: \( 103 - 80 = 23 \)
The cost increases by $23 for each additional day.
### Step 2: Formulate the function rule
Given that the increase per day is $23, we can express the total cost as:
- Initial cost for the first day: $34
- Additional cost for each additional day: \( 23d \)
However, we need to find the correct relationship that includes a fixed initial cost. It appears that $34 corresponds to the cost when renting for 1 day, which suggests we can derive the formula as follows:
The correct formula can be inferred as:
\[ c = 23d + 11 \]
### Step 3: Check the formula with the given values
1. For \( d = 1 \):
\[ c = 23(1) + 11 = 23 + 11 = 34 \]
2. For \( d = 2 \):
\[ c = 23(2) + 11 = 46 + 11 = 57 \]
3. For \( d = 3 \):
\[ c = 23(3) + 11 = 69 + 11 = 80 \]
4. For \( d = 4 \):
\[ c = 23(4) + 11 = 92 + 11 = 103 \]
All values match the cost given in the table.
### Conclusion
The function rule that represents the cost to rent a truck based on the number of days is:
\[ \boxed{c = 23d + 11} \]