document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125093>Question 1125093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 8-inch tall sunflower is planted in a garden and the height of the sunflower increases exponentially. 4 days after being planted the sunflower is 12.1446 inches tall. \r<BR>\n" );
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document.write( "a. What is the 4-day growth factor for the height of the sunflower?\r<BR>\n" );
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document.write( "b. What is the 1-day growth factor for the height of the sunflower?\r<BR>\n" );
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document.write( "c. What is the 6-day growth factor for the height of the sunflower? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741433 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=741433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the growth rate is exponential, therefore f = p * (1 + r) ^ n applies.\r<BR>\n" );
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document.write( "p is the present value = 8<BR>\n" );
document.write( "f is the future value = 12.1446.<BR>\n" );
document.write( "n is equal to 4 days.<BR>\n" );
document.write( "you want to solve for r.\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n becomes 12.1446 = 8 * (1 + r) ^ 4\r<BR>\n" );
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document.write( "divide both sides of the formula by 8 to get 12.1446 / 8 = (1 + r) ^ 4\r<BR>\n" );
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document.write( "take the fourth root of both sides of the equation to get (12.1446 / 8) ^ (1/4) = 1 + r\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get (12.1446 / 8) ^ (1/4) = 1 = r\r<BR>\n" );
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document.write( "solve for r to get r = .110000839\r<BR>\n" );
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document.write( "1 + r is the 1 day exponential growth factor = 1.110000839.\r<BR>\n" );
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document.write( "the 4 day exponential growth factor is 1.110000839 ^ 4 = 1.518075.\r<BR>\n" );
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document.write( "the 6 day exponential growth factor is 1.110000839 ^ 6 = 1.870423035.\r<BR>\n" );
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document.write( "to find the growth factor, you assume the present value is 1.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "1 * (1 + .110000839) ^ 4 = 1.518075.\r<BR>\n" );
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document.write( "the growth factor is then applied to the real present value.\r<BR>\n" );
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document.write( "in this case, the real present value was 8.\r<BR>\n" );
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document.write( "8 * (1 + .110000839) ^ 4 = 8 * 1.518075 = 12.1446.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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