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:
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For the first hour (0 < t ≤ 1):
- The cost is $5.
- This can be expressed as: \[ G(t) = 5 \quad \text{for } 0 < t \leq 1 \]
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For up to 2 hours (1 < t ≤ 2):
- The cost is a flat rate of $10.
- This can be expressed as: \[ G(t) = 10 \quad \text{for } 1 < t \leq 2 \]
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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.
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