To solve this problem, we need to analyze the cost function [tex]\( c(x) \)[/tex] related to Michelle's movie rental, where [tex]\( x \)[/tex] represents the number of nights she keeps the movie.
Given:
- A flat fee of \[tex]$1.50 when renting the movie.
- An additional \$[/tex]1.25 for each night she keeps the movie.
To develop the cost function [tex]\( c(x) \)[/tex], we combine both components:
1. The flat fee of \[tex]$1.50 will be paid regardless of the number of nights.
2. The cost increases by \$[/tex]1.25 for each night [tex]\( x \)[/tex].
Therefore, the cost function [tex]\( c(x) \)[/tex] can be expressed as:
[tex]\[ c(x) = 1.50 + 1.25 \cdot x \][/tex]
Now, let's review the given options:
- [tex]\( c(x) = 1.50 + 1.25 x \)[/tex]: Correct. It accurately represents the initial flat fee plus the variable cost per night.
- [tex]\( c(x) = 1.50 x + 1.25 \)[/tex]: Incorrect. This incorrectly multiplies the flat fee by the number of nights, which is not how the fee is structured.
- [tex]\( c(x) = 2.75 \)[/tex]: Incorrect. This seems to be a miscalculation or a misunderstanding of how fees are structured.
- [tex]\( c(x) = (1.50 + 1.25) x \)[/tex]: Incorrect. This incorrectly suggests that the flat fee and the nightly fee are multiplied by the number of nights.
Therefore, the correct answer is:
[tex]\[ c(x) = 1.50 + 1.25 x \][/tex]
