To solve for the total cost [tex]\( C \)[/tex] of renting a bicycle for [tex]\( h \)[/tex] hours, given that the cost is [tex]$9 for the first hour and $[/tex]4 for each additional hour, let's go through the problem step-by-step.
### Understanding the Charges:
1. First hour cost: The cost for the first hour is fixed at [tex]$9.
2. Additional hours cost: Each additional hour after the first is $[/tex]4 per hour.
### Forming the Equation:
To form the equation for the total cost, we need to consider two scenarios:
- If [tex]\( h = 1 \)[/tex] hour: The cost is simply [tex]$9.
- If \( h > 1 \) hours: The cost is $[/tex]9 for the first hour plus [tex]$4 for each additional hour beyond the first hour.
To generalize this for \( h \) hours, we can break it down as:
- The first hour always costs $[/tex]9.
- For [tex]\( h \)[/tex] hours, where [tex]\( h > 1 \)[/tex], there will be [tex]\( h - 1 \)[/tex] additional hours.
So, the total cost [tex]\( C \)[/tex] can be represented as:
[tex]\[ C = 9 + 4(h-1) \][/tex]
Expanding this equation:
[tex]\[ C = 9 + 4h - 4 \][/tex]
[tex]\[ C = 4h + 5 \][/tex]
Wait a moment! This is not matching option C exactly. Let's check another form:
[tex]\[ C = 4(h - 1) + 9 \][/tex]
This directly accounts for the first hour cost and additional hour costs in a simplified form.
Therefore, the correct representation of the situation is:
[tex]\[ C = 4(h - 1) + 9 \][/tex]
### Answer Options:
Let's analyze the given options:
- A. [tex]\( C = 13h \)[/tex]
- This implies [tex]$13 per hour for every hour, which is incorrect.
- B. \( C = 4h + 9 \)
- This implies $[/tex]4 for every hour plus an additional [tex]$9, which doesn't separate the first hour correctly.
- C. \( C = 4(h - 1) + 9 \)
- This matches our detailed modeling of the situation.
- D. \( C = 9h + 4 \)
- This implies $[/tex]9 for each hour plus an additional $4, which is incorrect.
Thus, the correct representation that matches the renting cost structure is:
[tex]\[ \boxed{C} \][/tex]
So, the correct answer is option C.
