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

Answer 1

To define the cost function \( G(t) \) based on the given parking garage rates, we can break it down as follows:

1. For \( t \) less than or equal to 1 hour: \[ G(t) = 5 \]

2. For \( t \) greater than 1 hour but less than or equal to 2 hours: \[ G(t) = 10 \]

3. For \( t \) greater than 2 hours (up to 24 hours): \[ G(t) = 12 \]

Thus, the complete piecewise cost function \( G(t) \) can be written as:

\[ G(t) = \begin{cases} 5 & \text{if } 0 < t \leq 1 \ 10 & \text{if } 1 < t \leq 2 \ 12 & \text{if } 2 < t \leq 24 \end{cases} \]

This function adequately represents the costs associated with parking as dictated by the garage's pricing policy. Note that \( G(t) \) does not cover \( t \) values that are 0 or negative, as they do not apply to the parking service.