document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164606>Question 1164606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a piecewise function for the given situation.\r<BR>\n" );
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document.write( "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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854343 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2264)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To write this piecewise function, we define the cost $C$ based on the number of hours $t$ spent in the garage.\r<BR>\n" );
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document.write( "### **1. Identify the Conditions**<BR>\n" );
document.write( "* **The Hourly Rate:** The garage charges **$2$** per hour. This is represented by $2t$.<BR>\n" );
document.write( "* **The Maximum Cap:** Once the cost reaches **$16$**, the price stops increasing. <BR>\n" );
document.write( "* **The \"Switch\" Point:** To find when the cap kicks in, we solve $2t = 16$. This happens at **$t = 8$** hours.\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### **2. The Piecewise Function**\r<BR>\n" );
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document.write( "Let $C(t)$ be the total cost in dollars and $t$ be the time in hours ($t \ge 0$):\r<BR>\n" );
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document.write( "$$C(t) = <BR>\n" );
document.write( "\begin{cases} <BR>\n" );
document.write( "2t & 0 \le t < 8 \\<BR>\n" );
document.write( "16 & t \ge 8<BR>\n" );
document.write( "\end{cases}$$\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### **3. Breakdown of the Function**<BR>\n" );
document.write( "* **$2t$ 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.<BR>\n" );
document.write( "* **$16$ 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.\r<BR>\n" );
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document.write( "### **Quick Check**<BR>\n" );
document.write( "If you stay for **5 hours**: $C(5) = 2(5) = \$10$.<BR>\n" );
document.write( "If you stay for **10 hours**: $C(10) = \$16$ (since $10 > 8$).\r<BR>\n" );
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document.write( "Does your specific parking problem require you to account for partial hours (like rounding up to the next hour), or is it strictly linear? </SPAN>\n" );
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