Answer :
Sure, let's go through how to write the formula step-by-step.
The problem states that a rental car company charges:
1. A fixed fee of \[tex]$95 (this is a one-time charge).
2. An additional fee of \$[/tex]47 per day (this is a variable charge depending on the number of days you rent the car).
We need to express the total cost [tex]\( C \)[/tex] as a function of the number of days [tex]\( d \)[/tex].
### Step-by-Step Solution:
1. Identify the Fixed Cost:
- The company charges a fixed fee of \[tex]$95, regardless of how many days the car is rented. This remains constant.
- Therefore, the fixed cost is \( 95 \) dollars.
2. Identify the Variable Cost:
- For each day \( d \) the car is rented, the company charges an additional \$[/tex]47.
- Hence, the variable cost per day is [tex]\( 47 \)[/tex].
3. Write the Formula:
- The total cost [tex]\( C \)[/tex] is the sum of the fixed cost and the variable cost multiplied by the number of days [tex]\( d \)[/tex].
- Mathematically, this can be written as:
[tex]\[
C(d) = 47d + 95
\][/tex]
So, the correct formula that expresses the total cost [tex]\( C \)[/tex] as a function of the number of days [tex]\( d \)[/tex] the car is rented is:
[tex]\[
C(d) = 47d + 95
\][/tex]
This means that if you know the number of days you are renting the car, you can plug in that value for [tex]\( d \)[/tex] in the formula to find out the total cost [tex]\( C \)[/tex].
The problem states that a rental car company charges:
1. A fixed fee of \[tex]$95 (this is a one-time charge).
2. An additional fee of \$[/tex]47 per day (this is a variable charge depending on the number of days you rent the car).
We need to express the total cost [tex]\( C \)[/tex] as a function of the number of days [tex]\( d \)[/tex].
### Step-by-Step Solution:
1. Identify the Fixed Cost:
- The company charges a fixed fee of \[tex]$95, regardless of how many days the car is rented. This remains constant.
- Therefore, the fixed cost is \( 95 \) dollars.
2. Identify the Variable Cost:
- For each day \( d \) the car is rented, the company charges an additional \$[/tex]47.
- Hence, the variable cost per day is [tex]\( 47 \)[/tex].
3. Write the Formula:
- The total cost [tex]\( C \)[/tex] is the sum of the fixed cost and the variable cost multiplied by the number of days [tex]\( d \)[/tex].
- Mathematically, this can be written as:
[tex]\[
C(d) = 47d + 95
\][/tex]
So, the correct formula that expresses the total cost [tex]\( C \)[/tex] as a function of the number of days [tex]\( d \)[/tex] the car is rented is:
[tex]\[
C(d) = 47d + 95
\][/tex]
This means that if you know the number of days you are renting the car, you can plug in that value for [tex]\( d \)[/tex] in the formula to find out the total cost [tex]\( C \)[/tex].
