To determine the correct equation representing the total cost [tex]\( C \)[/tex] of renting a canoe for [tex]\( h \)[/tex] hours, given that it costs \[tex]$8 for the first hour and \$[/tex]3 for each additional hour, let's analyze each option step by step.
First, let's break down the cost structure:
- The first hour costs \[tex]$8.
- Each additional hour costs \$[/tex]3.
Now, let's evaluate each option:
### Option A: [tex]\( C = 8h + 3 \)[/tex]
- This implies that each of the [tex]\( h \)[/tex] hours costs \[tex]$8, plus an additional flat fee of \$[/tex]3.
- This would mean for any number of hours [tex]\( h \)[/tex], the cost calculation is [tex]\( C = 8h + 3 \)[/tex].
- For [tex]\( h = 1 \)[/tex]: [tex]\( C = 8 \times 1 + 3 = \$11 \)[/tex].
- The first hour should cost \[tex]$8. Thus, this option does not correctly represent the given cost structure.
### Option B: \( C = 3(h - 1) + 8 \)
- This correctly captures the cost structure:
- \( C = 3(h-1) \) represents the cost for the additional hours.
- Adding 8 accounts for the cost of the first hour.
- Let’s test this with \( h = 1 \) and \( h = 3 \):
- For \( h = 1 \): \( C = 3(1 - 1) + 8 = 3(0) + 8 = \$[/tex]8 \).
- For [tex]\( h = 3 \)[/tex]: [tex]\( C = 3(3 - 1) + 8 = 3(2) + 8 = 6 + 8 = \$14 \)[/tex].
- This method accurately represents the cost structure.
### Option C: [tex]\( C = 3h + 8 \)[/tex]
- This implies a flat fee of \[tex]$8 plus \$[/tex]3 for each of the [tex]\( h \)[/tex] hours.
- For [tex]\( h = 1 \)[/tex]: [tex]\( C = 3 \times 1 + 8 = 3 + 8 = \$11 \)[/tex].
- The first hour should only cost \[tex]$8, thus this option does not correctly represent the given cost structure.
### Option D: \( C = 11h \)
- This represents a rate of \$[/tex]11 for each hour.
- For [tex]\( h = 1 \)[/tex]: [tex]\( C = 11 \times 1 = \$11 \)[/tex].
- For [tex]\( h = 2 \)[/tex]: [tex]\( C = 11 \times 2 = \$22 \)[/tex].
- This does not match the cost structure provided.
From the above analysis, it is clear that option B ([tex]\( C = 3(h - 1) + 8 \)[/tex]) correctly represents the given scenario.
Therefore, the correct answer is:
[tex]\( \boxed{B} \)[/tex]
