document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205120>Question 1205120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold seven cars (P0=7). The second week the dealership sold fifteen cars (p1=15).\r<BR>\n" );
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document.write( "Write the recursive formula for the number of cars sold, <BR>\n" );
document.write( "Pn, in the (N+ 1)th week.\r<BR>\n" );
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document.write( "Pn=Pn+ Blank<BR>\n" );
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document.write( "Write the explicit formula for the number of cars sold, Pn, in the (N+1)th week.\r<BR>\n" );
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document.write( " Pn=     N+   \r<BR>\n" );
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document.write( "If this trend continues, how many cars will be sold in the sixth week?\r<BR>\n" );
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document.write( "blank cars\r<BR>\n" );
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document.write( "In each box, enter a single number. Do not leave any boxes blank (enter 1 or 0 as appropriate if necessary) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841762 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The statement of the problem has (at least) three faults.<br><BR>\n" );
document.write( "(1) \"n\" and \"N\" are used interchangeably to represent the same thing.<BR>\n" );
document.write( "(2) The form \"Pn=Pn+ Blank\" is not appropriate for a recursive formula.  In fact, if that form is correct, then \"Blank\" is 0.<BR>\n" );
document.write( "(3) The form \"Pn= N+\" is not appropriate for an explicit formula.<br><BR>\n" );
document.write( "Since the number sold in week 1 is P(0), the number sold in week (n+1) is P(n).<br><BR>\n" );
document.write( "Part 1 -- recursive formula<br><BR>\n" );
document.write( "The recursive formula for the number sold in week (n+1) tells the number sold as a function of the number sold in week n.  The number sold in week n is P(n-1); and since the number sold increases by the same number 8 in each week, the recursive formula for the number sold in week (n+1) is<br><BR>\n" );
document.write( "P(n)=P(n-1)+8<br><BR>\n" );
document.write( "Part 2 -- explicit formula<br><BR>\n" );
document.write( "The explicit formula for the number sold in week (n+1) is a linear equation in the form<br><BR>\n" );
document.write( "y=mx+b<br><BR>\n" );
document.write( "or, in this problem,<br><BR>\n" );
document.write( "P(n)=mn+b<br><BR>\n" );
document.write( "Since the number sold increases by 8 each week, m=8; and since P(0)=7, b=7 and the formula is<br><BR>\n" );
document.write( "P(n)=8n+7<br><BR>\n" );
document.write( "Part 3 -- number sold in week 6<br><BR>\n" );
document.write( "The number sold in week 6 is<br><BR>\n" );
document.write( "P(5) = 8(5)+7 = 47<br><BR>\n" );
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