Alright, let's take a close look at the problem and identify which equation correctly represents the given parking cost scenario. We know two key pieces of information about the parking garage's pricing policy:
1. The first hour is free.
2. For each additional hour or fraction of an hour beyond the first hour, there is a charge of \[tex]$2.50.
To find the correct equation, we need to incorporate these details:
- Analysis:
- For \( x \) hours of parking time:
- If \( x \leq 1 \), the cost should be \$[/tex]0 because the first hour is free.
- If [tex]\( x > 1 \)[/tex], the cost should be \[tex]$2.50 for each hour or fraction of an hour beyond the first hour.
Keeping that in mind, we start by looking at each option:
1. \( f(x) = 2.50 \lceil x \rceil \)
- This expression means charging \$[/tex]2.50 for every ceiling value of [tex]\( x \)[/tex]. Since the first hour is free, this does not fit our criteria.
2. [tex]\( f(x) = 2.50 + \lceil x \rceil \)[/tex]
- This expression does not fit the condition since it starts the cost at \[tex]$2.50 plus an added amount for the ceiling value of \( x \), not respecting the first hour free rule.
3. \( f(x) = 250 |x-1| \)
- This expression is not appropriate because it uses 250 (not 2.50) and does not correctly model the parking cost structure described.
4. \( f(x) = 2.50 [x+1] \)
- This uses square brackets, which typically mean the floor function, and does not match the ceiling operation needed to cover fractions of hours beyond the second.
Given that none of these fits perfectly, here is what the correct function should look like based on the scenario:
- For \( x \leq 1 \), the cost \( f(x) \) should be \$[/tex]0.
- For [tex]\( x > 1 \)[/tex], the cost [tex]\( f(x) \)[/tex] should be \$2.50 multiplied by the ceiling of [tex]\( x - 1 \)[/tex].
Hence, the best way to describe this mathematically:
[tex]\[ f(x) = 2.50 \cdot \lceil x - 1 \rceil \][/tex]
So the correct answer should be modified from the given options to meet this requirement.
