document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200984>Question 1200984</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 eight cars (P0=8). The second week the dealership sold nine cars (P1=9).\r<BR>\n" );
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document.write( "Write the recursive formula for the number of cars sold, PN, in the (N+1)th week.\r<BR>\n" );
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document.write( "PN= ____ PN−1+ _____<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+ ____<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( "____ cars </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835210 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> since the number of cars sold each week is 1 more than the number of cars sold the previous week:\r<BR>\n" );
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document.write( "the recursive formula is p(n) = p(n-1) + 1<BR>\n" );
document.write( "you have to know what p(n-1) is before you can find p(n)<BR>\n" );
document.write( "for example, if p(n-1) is 8, then p(n) is 9.\r<BR>\n" );
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document.write( "the explicit formula is p(n) = n + p(0).<BR>\n" );
document.write( "you do not need to know what p(n-1) is before you can find p(n).<BR>\n" );
document.write( "you only need to know what p(0) is.\r<BR>\n" );
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document.write( "in this problem, p(0) is assumed to be 8.<BR>\n" );
document.write( "if you want to know what p(3) is, you can't find it using the recursive formula because you don't know what p(2) is.\r<BR>\n" );
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document.write( "you can find it using the explicit formula, as long as you know what p(0) is.<BR>\n" );
document.write( "when p(0) = 8, the explicit formula becomes p(n) = n + 8<BR>\n" );
document.write( "when n = 3, the explicit formula tells you that p(3) = 3 + 8 = 11.\r<BR>\n" );
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document.write( "if you use the explicit formula to find p(2), then you can use the recursive formula to find p(3).<BR>\n" );
document.write( "p(2) = 2 + 8 = 10<BR>\n" );
document.write( "p(3) = p(2) + 1 = 10 + 1 = 11.\r<BR>\n" );
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document.write( "the number of cars sold in the 6th week would use the explicit fromula of p(n) = n + 8 to get p(6) = 6 + 8 = 14.\r<BR>\n" );
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