To solve for the initial admission fee of the Trampoline Park, we need to find the starting value on the graph of the cost function. This function will typically have the form [tex]\( C = mH + b \)[/tex], where:
- [tex]\( C \)[/tex] is the total cost.
- [tex]\( m \)[/tex] is the hourly fee.
- [tex]\( H \)[/tex] is the number of hours.
- [tex]\( b \)[/tex] is the initial admission fee, which we need to determine.
Given the information:
- The hourly fee is [tex]\( \$ 4.50 \)[/tex].
Let's analyze the cost function. The total cost at any given number of hours can be calculated by adding [tex]\( \$ 4.50 \)[/tex] for each hour to the initial admission fee. We know that the options for the initial value [tex]\( b \)[/tex] are:
- [tex]\( \$ 4.50 \)[/tex]
- [tex]\( \$ 5.00 \)[/tex]
- [tex]\( \$ 5.50 \)[/tex]
- [tex]\( \$ 6.00 \)[/tex]
We need to determine which of these values represents the correct starting cost when no hours have been spent at the trampoline park.
Upon analyzing the problem and the options provided, we find that the initial admission fee charged by the trampoline park is:
[tex]\[ \$ 6.00 \][/tex]
Thus, the initial value or the initial admission fee for the trampoline park is [tex]\( \$ 6.00 \)[/tex].
