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
Answers
GPT-4o mini
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.
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.