document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183096>Question 1183096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Having trouble using the example already posted on this site to solve this equation, please help.\r<BR>\n" );
document.write( "\n" );
document.write( "A population grows according to an exponential growth model, with P0=40 and P1=48\r<BR>\n" );
document.write( "\n" );
document.write( "Complete the recursive formula:\r<BR>\n" );
document.write( "\n" );
document.write( "Pn = ×Pn−1\r<BR>\n" );
document.write( "\n" );
document.write( "Write an explicit formula for Pn\r<BR>\n" );
document.write( "\n" );
document.write( "Pn = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813258 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=813258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "P0 is the first population value, and it's 40<BR>\n" );
document.write( "P1 is the second population value, and it's 48<BR>\n" );
document.write( "Dividing the values gets us P1/P0 = 48/40 = 1.2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bn%5D+=+1.2%2AP%5Bn-1%5D ALIGN=MIDDLE  ALT=\"P%5Bn%5D+=+1.2%2AP%5Bn-1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "meaning: \"to get the current population, we multiply the previous population by 1.2\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This wraps up the recursive formula. As with any recursion problem, don't forget to mention the starting value. \r<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now onto the explicit formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We found that 1.2 is the multiplier from the last section. This is the value of b in y = a*b^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The value of 'a' is the starting value, so a = 40\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we have y = a*b^x update to y = 40*(1.2)^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then we'll replace x with n, and replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bn%5D ALIGN=MIDDLE  ALT=\"P%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bn%5D+=+40%2A%281.2%29%5En ALIGN=MIDDLE  ALT=\"P%5Bn%5D+=+40%2A%281.2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's try plugging in n = 0 and see what we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bn%5D+=+40%2A%281.2%29%5En ALIGN=MIDDLE  ALT=\"P%5Bn%5D+=+40%2A%281.2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B0%5D+=+40%2A%281.2%29%5E0 ALIGN=MIDDLE  ALT=\"P%5B0%5D+=+40%2A%281.2%29%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B0%5D+=+40%2A%281%29 ALIGN=MIDDLE  ALT=\"P%5B0%5D+=+40%2A%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B0%5D+=+40 ALIGN=MIDDLE  ALT=\"P%5B0%5D+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So far, so good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now try n = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bn%5D+=+40%2A%281.2%29%5En ALIGN=MIDDLE  ALT=\"P%5Bn%5D+=+40%2A%281.2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D+=+40%2A%281.2%29%5E1 ALIGN=MIDDLE  ALT=\"P%5B1%5D+=+40%2A%281.2%29%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D+=+40%2A%281.2%29 ALIGN=MIDDLE  ALT=\"P%5B1%5D+=+40%2A%281.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D+=+48 ALIGN=MIDDLE  ALT=\"P%5B1%5D+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That works as well. So the answer is confirmed.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );