document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145308>Question 145308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please disregard this previous question I submitted. Thank you for your help.\r<BR>\n" );
document.write( "\n" );
document.write( "I am to recall that, when interest is compounded continuously, the balance in an account after t years is given by <BR>\n" );
document.write( "A = Pe^rt,<BR>\n" );
document.write( "where P is the initial investment and r is the interest rate.\r<BR>\n" );
document.write( "\n" );
document.write( "Evaluate each of the functions below at x = 1, 2, 4, 8, and 16.  Plot the graph of each function.  Classify each as linear, quadratic, polynomial, exponential, or logarithmic, and explain the reasons for your classifications.  Compare how quickly each function increases, based on the evaluations and graphs, and rank the functions from fastest to slowest growing.  <BR>\n" );
document.write( "- f(x) = x3 - 3x2 - 2x + 1<BR>\n" );
document.write( "- f(x) = ex<BR>\n" );
document.write( "- f(x) = 3x - 2<BR>\n" );
document.write( "- f(x) = log x<BR>\n" );
document.write( "- f(x) = x2 - 5x + 6\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105978 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=105978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E3+-+3x%5E2+-+2x+%2B+1 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3+-+3x%5E2+-+2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(1)=-3, f(2)=-7, f(4)=9, f(8)=305, f(16)=3,297\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+-+3x%5E2+-+2x+%2B+1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+-+3x%5E2+-+2x+%2B+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=e%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(1)=2.71828, f(2)=7.38906, f(4)=54.59815, f(8)=2980.9579, f(16)=8886110.5205\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+exp%28x%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+exp%28x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x) = 3x - 2 :\r<BR>\n" );
document.write( "\n" );
document.write( "f(1)=1, f(2)=4, f(4)=10, f(8)=22, f(16)=46\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3x+-+2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3x+-+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x)=log(x):\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(1)=0, f(2)=0.30103, f(4)=0.60206, f(8)=0.90309, f(16)=1.20412\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+log%2810%2Cx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+log%2810%2Cx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x) = x^2 - 5x + 6:\r<BR>\n" );
document.write( "\n" );
document.write( "f(1)=2, f(2)=0, f(4)=2, f(8)=30, f(16)=182\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+-+5x+%2B+6%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+-+5x+%2B+6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Rank from fastest growing to slowest growing:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=e%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3+-+3x%5E2+-+2x+%2B+1 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3+-+3x%5E2+-+2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2+-+5x+%2B+6 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2+-+5x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x-2 ALIGN=MIDDLE  ALT=\"f%28x%29=3x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=log%28%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=log%28%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );