Alright, let's break down the problem and derive the linear function step-by-step.
1. Identify the fixed daily rental cost:
The cost of renting the car for one day is a fixed amount of [tex]$35. This means that no matter how many miles you drive, you always have to pay this daily rental fee.
2. Identify the variable cost per mile:
In addition to the daily rental fee, you also have to pay $[/tex]0.07 for each mile you drive. Thus, the more miles you drive, the higher this part of the cost will be.
3. Define the cost function:
Let's denote the total cost of renting the car for one day as [tex]\( C \)[/tex], and the number of miles driven as [tex]\( x \)[/tex].
4. Combine the fixed and variable costs:
- The fixed cost is [tex]$35.
- The variable cost is $[/tex]0.07 per mile, which translates to [tex]\( 0.07x \)[/tex] dollars if [tex]\( x \)[/tex] is the number of miles driven.
5. Write the linear function:
To express the total cost [tex]\( C \)[/tex] as a function of the number of miles [tex]\( x \)[/tex]:
[tex]\[
C(x) = 35 + 0.07x
\][/tex]
So, the linear function that expresses the total cost [tex]\( C \)[/tex] of renting the car for one day as a function of the number of miles driven [tex]\( x \)[/tex] is:
[tex]\[
C(x) = 35 + 0.07x
\][/tex]
This function tells us that for every mile driven, the cost increases by [tex]$0.07, in addition to the fixed daily rental fee of $[/tex]35.
