To determine the cost [tex]\( C \)[/tex] of a ride of [tex]\( m \)[/tex] miles for the Get-Around Cab Company, we need to consider two components:
1. Initial cost upon entry: This is a fixed cost that you pay as soon as you use the service, which is \[tex]$2.50.
2. Cost per mile: This is the amount charged per mile of distance traveled, which is \$[/tex]2 per mile.
To write the function [tex]\( C(m) \)[/tex] that calculates the total cost based on the number of miles [tex]\( m \)[/tex] traveled, follow these steps:
1. Initial cost: The fixed initial fee is \[tex]$2.50.
2. Variable cost: The cost per mile is \$[/tex]2, so for [tex]\( m \)[/tex] miles, this would be [tex]\( 2 \times m \)[/tex].
Thus, the total cost [tex]\( C \)[/tex] can be expressed as the sum of the initial cost and the cost for [tex]\( m \)[/tex] miles.
Putting it into the function form:
[tex]\[
C(m) = 2 m + 2.5
\][/tex]
So, the function [tex]\( C(m) \)[/tex] that determines the total cost [tex]\( C \)[/tex] of a ride for [tex]\( m \)[/tex] miles is:
[tex]\[
C(m) = 2m + 2.5
\][/tex]
This function combines the initial entry cost of \[tex]$2.50 with the additional cost of \$[/tex]2 per mile.
