Garage charges one time rate of $8 plus $1.50 per half hour. What function represents total cost C(x), for parking for x hours
c(x) = 8 + 1.5x
To determine the function that represents the total cost \(C(x)\) for parking for \(x\) hours at the garage, we need to consider the given rates and conditions.
We are given that the garage charges a one-time rate of $8 plus $1.50 per half hour. This means that there is a fixed cost of $8 for any period of parking, regardless of the length. Additionally, there is an additional charge of $1.50 for each half hour of parking.
Let's break down the total cost based on the length of parking:
For the fixed rate of $8, this cost is constant and does not change based on the length of parking. So, we can consider this as the initial cost.
The additional charge per half hour parking is $1.50. Since there are 2 half hours in each hour, the number of half hours of parking is \(2x\).
The cost for the additional half hours is then \(1.50 \times 2x = 3x\) dollars.
Adding these two components together, we get the function for the total cost \(C(x)\):
\[C(x) = 8 + 3x\]
Therefore, the function that represents the total cost \(C(x)\) for parking for \(x\) hours in the garage is \(C(x) = 8 + 3x\).