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

Question

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: $$G(t)=5\text{for }0<t\le 1$$

2. For up to 2 hours (1 < t ≤ 2):

   • The cost is a flat rate of $10.
   • This can be expressed as: $$G(t)=10\text{for }1<t\le 2$$

3. For the entire day (t > 2):

   • The cost is an all-day fee of $12.
   • This can be expressed as: $$G(t)=12\text{for }t>2$$

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

$$G(t)=\{\begin{array}{llll}5& \text{if }0<t\le 110& \text{if }1<t\le 212& \text{if }t>2\end{array}$$

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.