Let's break down the problem step-by-step to understand how the cost function is formulated based on the scenario provided.
1. Identify the flat fee and nightly charge:
- Flat fee: Michelle pays a flat fee of [tex]$1.50 to rent a movie.
- Nightly charge: Additionally, she pays $[/tex]1.25 for each night she keeps the movie.
2. Define the variable:
- Let [tex]\( x \)[/tex] be the number of nights Michelle keeps the movie.
3. Formulate the cost function:
- The total cost [tex]\( c(x) \)[/tex] has two components:
- The flat fee of [tex]$1.50, which is constant regardless of the number of nights.
- An additional charge of $[/tex]1.25 per night, which changes proportionally with the number of nights [tex]\( x \)[/tex].
4. Combine the components into one function:
- The flat fee component remains as [tex]$1.50.
- The nightly charge component is $[/tex]1.25 times the number of nights [tex]\( x \)[/tex], which can be written as [tex]\( 1.25x \)[/tex].
5. Summing these components:
- The total cost function [tex]\( c(x) \)[/tex] is the sum of the flat fee and the nightly charges:
[tex]\[
c(x) = 1.50 + 1.25x
\][/tex]
Upon examining the given choices, the correct choice of the cost function that represents this scenario is:
[tex]\[
c(x) = 1.50 + 1.25x
\][/tex]
Thus, the correct answer is:
[tex]$
c(x) = 1.50 + 1.25x
$[/tex]
This function correctly encapsulates the flat rental fee and the additional nightly charges specified in the problem.
