The question requires us to represent the total cost [tex]\( C \)[/tex] of renting a kayak for [tex]\( h \)[/tex] hours, based on the rates given: \[tex]$12 for the first hour and \$[/tex]5 for each additional hour.
Let's break down the problem step-by-step:
1. Understand the components of the cost:
- The cost for the first hour of renting the kayak is \[tex]$12.
- For each additional hour after the first hour, the cost increases by \$[/tex]5.
2. Define the total cost [tex]\( C \)[/tex]:
- When [tex]\( h = 1 \)[/tex] (renting for only 1 hour), the total cost is simply the initial cost of \[tex]$12.
- For \( h > 1 \), we need to account for the additional hours. The total number of additional hours beyond the first hour is \( h - 1 \). The cost for these additional hours is \( 5 \times (h - 1) \).
3. Construct the total cost expression:
- The total cost \( C \) can be written as the sum of the initial cost for the first hour and the cost of the additional hours:
\[
C = 12 + 5(h - 1)
\]
This equation captures the initial \$[/tex]12 charge and adds the additional cost for renting beyond the first hour.
4. Simplify the expression:
[tex]\[
C = 12 + 5(h - 1) = 12 + 5h - 5 = 5h + 7
\][/tex]
So, the total cost [tex]\( C \)[/tex] of renting a kayak for [tex]\( h \)[/tex] hours is represented by the equation:
[tex]\[
C = 5h + 7
\][/tex]
The answer corresponds to option B, which is:
[tex]\[
C = 5(h - 1) + 12
\][/tex]
Thus, the correct answer is [tex]\( \boxed{B} \)[/tex].
