SOLUTION: Write a piecewise function for the given situation. A parking garage charges $2 an hour for parking in the garage with a maximum amount of money you can be charged is $16 no mat

Question 1164606: Write a piecewise function for the given situation.
A parking garage charges $2 an hour for parking in the garage with a maximum amount of money you can be charged is $16 no matter the amount time you parked there.
Answer by CPhill(2264) (Show Source): You can put this solution on YOUR website!
To write this piecewise function, we define the cost $C$ based on the number of hours $t$ spent in the garage.
### **1. Identify the Conditions**
* **The Hourly Rate:** The garage charges **$2$** per hour. This is represented by $2t$.
* **The Maximum Cap:** Once the cost reaches **$16$**, the price stops increasing.
* **The "Switch" Point:** To find when the cap kicks in, we solve $2t = 16$. This happens at **$t = 8$** hours.
---
### **2. The Piecewise Function**
Let $C(t)$ be the total cost in dollars and $t$ be the time in hours ($t \ge 0$):
$$C(t) =
\begin{cases}
2t & 0 \le t < 8 \\
16 & t \ge 8
\end{cases}$$
---
### **3. Breakdown of the Function**
* **$2t$ for $0 \le t < 8$:** If you stay for less than 8 hours, you pay exactly \$2 for every hour parked. For example, 3 hours costs \$6.
* **$16$ for $t \ge 8$:** Once you hit the 8-hour mark, the "flat rate" applies. Whether you stay for 9 hours, 12 hours, or 24 hours, the price remains stuck at \$16.
### **Quick Check**
If you stay for **5 hours**: $C(5) = 2(5) = \$10$.
If you stay for **10 hours**: $C(10) = \$16$ (since $10 > 8$).
Does your specific parking problem require you to account for partial hours (like rounding up to the next hour), or is it strictly linear?
RELATED QUESTIONS
WRITE A PIECEWISE FUNCTION FOR THE GIVEN SITUATION AND THEN GRAPH IT. A PARKING GARAGE (answered by solver91311)

a parking garage charges 2 for the first hour and 0.75 for every hour after that. The... (answered by ewatrrr)

a parking garage charges $1.75 for the first hour and $0.25 for each parking from 10a.m... (answered by lenny460)

A parking garage charges $2.00 for the first hour and $1.25 for each additional hour. If... (answered by josgarithmetic)

Parking garage fees the Greenville City Garage charges $5 for the first hour and then... (answered by josmiceli)

A parking garage charges $1.50 for the 1st hour of parking and $0.75 for each additional... (answered by ikleyn)

You park your car in a parking garage for 6 hours. Your fee upon exiting the garage is... (answered by Alan3354)

Mary is certain that every time she parks in the municipal parking garage it cost her at... (answered by jorel1380)

you park your car in a parking lot for 6 hours. your fee upon leaving the garage is $42. (answered by JulietG)