document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=862065>Question 862065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In May 2003, a gas company had the given rate schedule for natural gas usage in single-family residences. <BR>\n" );
document.write( "Monthly service charge- 10.25<BR>\n" );
document.write( "1st 60 therms- 0.24228/therm<BR>\n" );
document.write( "Therms over 60- 0.23599/therm<BR>\n" );
document.write( "Gas Charge- 0.267/therm.<BR>\n" );
document.write( "Construct a function that relates the monthly charge C for x therms of gas. There are two pieces of the function: one that represents the total cost when 60 therms or fewer are used, and one that represents the total cost when more than 60 therms are used. <BR>\n" );
document.write( "First piece of the function, let x be the total number of therms used, and then add together all the constant charges. What does the first piece of the function look like? <BR>\n" );
document.write( "C= 10.25+0.24228x+0.2627x=10.25+.50498   for 0<x<60<BR>\n" );
document.write( "Using the same method, find the second piece of the function. Recall that the “Therms over 60” service charge needs to be added, which represents the cost of the additional therms over 60.<BR>\n" );
document.write( "What does the second function look like?<BR>\n" );
document.write( "C= 10.63+.49869x  for x>60.<BR>\n" );
document.write( "My question is what do you calculate to get 10.63?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #519436 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=519436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For therms up to 60, the function based on the listing of charges is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=10.25%2B0.24228x%2B0.267x ALIGN=MIDDLE  ALT=\"C=10.25%2B0.24228x%2B0.267x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=10.25%2B0.50928x%29 ALIGN=MIDDLE  ALT=\"highlight%28C=10.25%2B0.50928x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The information about \"Gas charge\" does not indicate if it is for more or less than 60 therms, so my best interpretation is to include it in both function branches.\r<BR>\n" );
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document.write( "For more than 60 therms, the function must be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=10.250.23559x%2B0.267x ALIGN=MIDDLE  ALT=\"C=10.250.23559x%2B0.267x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=10.25%2B0.74487x%29 ALIGN=MIDDLE  ALT=\"highlight%28C=10.25%2B0.74487x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "None of the information in the description gives any justification for  a term of 10.63 in the second branch of the function.\r<BR>\n" );
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document.write( "FURTHER THOUGHT:  For OVER 60 therms, you would have 60 therms plus x-60 therms.<BR>\n" );
document.write( " This may mean charge of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2A0.24228%2B%28x-60%29%2A%280.23599%29 ALIGN=MIDDLE  ALT=\"60%2A0.24228%2B%28x-60%29%2A%280.23599%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.5368%2B0.23599x-60%280.23599%29 ALIGN=MIDDLE  ALT=\"14.5368%2B0.23599x-60%280.23599%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.5368%2B0.23599x-14.1594 ALIGN=MIDDLE  ALT=\"14.5368%2B0.23599x-14.1594\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3774%2B0.23599x ALIGN=MIDDLE  ALT=\"0.3774%2B0.23599x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2810.25%2B0.3774=10.6274%29 ALIGN=MIDDLE  ALT=\"highlight%2810.25%2B0.3774=10.6274%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is to the nearest hundredths place, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2810.63%29 ALIGN=MIDDLE  ALT=\"highlight%2810.63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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