Question

A parking garage charges $5 for the first hour, $10 for up to 2 hours, and $12 for the entire day. Let G be the dollar cost of parking for t hours
Show your work all the steps

Answer 1

To express the dollar cost \( G \) of parking in terms of hours \( t \), we need to consider the different pricing brackets established by the parking garage:

1. **For the first hour (0 < t ≤ 1)**:
- The cost is $5.
- This can be expressed as:
\[
G(t) = 5 \quad \text{for } 0 < t \leq 1
\]

2. **For up to 2 hours (1 < t ≤ 2)**:
- The cost is a flat rate of $10.
- This can be expressed as:
\[
G(t) = 10 \quad \text{for } 1 < t \leq 2
\]

3. **For the entire day (t > 2)**:
- The cost is an all-day fee of $12.
- This can be expressed as:
\[
G(t) = 12 \quad \text{for } t > 2
\]

Now we can combine these pieces into a piecewise function that describes the cost \( G(t) \) based on the value of \( t \):

\[
G(t) =
\begin{cases}
5 & \text{if } 0 < t \leq 1 \\
10 & \text{if } 1 < t \leq 2 \\
12 & \text{if } t > 2
\end{cases}
\]

### Summary
Thus, the dollar cost \( G \) of parking for \( t \) hours is given by the piecewise function above, which covers all possible time intervals for parking based on the specified rates.