document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207185>Question 1207185</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mrs. Robinson made the table below showing the yearly balance of her savings<BR>\n" );
document.write( "account. Interest on the account compounds annually. Which of the following<BR>\n" );
document.write( "describes the best model to be used for Mrs. Robinson’s data?<BR>\n" );
document.write( "Year  Balance in Dollars<BR>\n" );
document.write( "0     $400<BR>\n" );
document.write( "5     $463.71<BR>\n" );
document.write( "10    $537.57<BR>\n" );
document.write( "15    $623.19<BR>\n" );
document.write( "20    $722.44<BR>\n" );
document.write( "25    $837.51\r<BR>\n" );
document.write( "\n" );
document.write( "A) a positive linear function<BR>\n" );
document.write( "B) a positive quadratic function<BR>\n" );
document.write( "C) an exponential growth function<BR>\n" );
document.write( "D) a positive absolute value function </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844918 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=844918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Use technology of your choice to determine these regression equations<ul><li>linear: f(x) = 17.4249142857x + 379.5919047619</li><li>quadratic: g(x) = 0.2559714286x^2 + 11.0256285714x + 400.9228571429</li><li>exponential: h(x) = 400.0011431092e^(0.0295586331x)</li></ul>The decimal values are approximate.<BR>\n" );
document.write( "The 'e' is a special constant roughly equal to 2.718<BR>\n" );
document.write( "h(x) is roughly equivalent to 400.0011431092*1.0299998258^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From here, use spreadsheet software to construct the following table<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD  colspan=2>Given</TD><TD  colspan=3>Absolute Error</TD></tr><tr><TD >x</TD><TD >y</TD><TD >linear</TD><TD >quadratic</TD><TD >exponential</TD></tr><tr><TD >0</TD><TD >400</TD><TD >20.408095</TD><TD >0.922857</TD><TD >0.001143</TD></tr><tr><TD >5</TD><TD >463.71</TD><TD >3.006476</TD><TD >1.259714</TD><TD >0.000563</TD></tr><tr><TD >10</TD><TD >537.57</TD><TD >16.271048</TD><TD >0.793714</TD><TD >0.002821</TD></tr><tr><TD >15</TD><TD >623.19</TD><TD >17.775619</TD><TD >0.710857</TD><TD >0.002834</TD></tr><tr><TD >20</TD><TD >722.44</TD><TD >5.65019</TD><TD >1.384</TD><TD >0.004115</TD></tr><tr><TD >25</TD><TD >837.51</TD><TD >22.295238</TD><TD >0.964286</TD><TD >0.000024</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "The first two columns are copy/pasted from the table your teacher gave you. Except of course the dollar sign symbols have been erased.<BR>\n" );
document.write( "The remaining 3 columns represent the absolute error when subtracting the stated y value from each regression output.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For example, when x = 0 the y value is y = 400.<BR>\n" );
document.write( "If you plugged x = 0 into the linear regression function, then you should find f(0) = 379.5919047619<BR>\n" );
document.write( "The error is approximately |y-f(x)| = |y-f(0)| = |400-379.5919047619| = 20.4080952381<BR>\n" );
document.write( "Follow similar steps to compute the other error values. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In a perfect world, the error would be 0. But of course nothing is ever perfect. <BR>\n" );
document.write( "The next best thing is to try to get as close to 0 as possible.<BR>\n" );
document.write( "This occurs with the exponential regression function. <BR>\n" );
document.write( "Therefore, the <font color=red>exponential</font> is the best fit.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red>choice C</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );