document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117437>Question 1117437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The table represents the total cost an online store charges for streaming movies. It charges an annual membership fee and a fee for each movie streamed. \r<BR>\n" );
document.write( "\n" );
document.write( "Movies Streamed- 0,1,2,3<BR>\n" );
document.write( "Total Cost- 52,55.40,58.80,62.20\r<BR>\n" );
document.write( "\n" );
document.write( "A local rental store uses the function C=4.60m to determine how much to charge for movie rentals. C is the total cost and m is the number of movies rented. The store does not charge customers a membership fee. If 50 movies are rented in a year, which option is cheaper? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732533 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=732533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large C_s(m)\"> represent the cost function for streaming <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> movies, and let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large C_r(m)\"> represent the cost function for renting <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> movies.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since for streaming zero movies the cost is $52, $52 is clearly the amount of the annual fee.  Then one movie costs 55.40, so just the movie is 3.40.  Two movies are 58.80, so two movies are 6.80, or two times 3.40. The cost of three movies fits the pattern, so we are reasonably certain that the function is linear and that the slope is 3.40 while the y-intercept is 52, hence:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ C_s(m)\ =\ 3.40m\ +\ 52\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And we are given the rental cost function directly:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ C_r(m)\ =\ 4.60m\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "All that you need to do is to calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large C_s(50)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large C_r(50)\"> and decide which is smaller.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Looking at the problem from an intuitive point of view, notice that if 52 movies were streamed, they would actually cost $4.40 each on an annualized basis, whereas the rentals are a fixed $4.60.  The question of which is cheaper at 50 movies rented should be obvious.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );