document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193275>Question 1193275</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MAT 145: Topics In Contemporary Math\r<BR>\n" );
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document.write( "             19: Solving Exponential Growth\r<BR>\n" );
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document.write( "1) The population of fuzzy quadrupeds doubles every month after they are introduced to a <BR>\n" );
document.write( "new region. Suppose 5 fuzzy quadrupeds are accidentally introduced to Springfield when <BR>\n" );
document.write( "a family visited the region to which fuzzy quadrupeds are native. How many months <BR>\n" );
document.write( "would it take for there to be 325 fuzzy quadrupeds in Springfield?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825278 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=825278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> growth factor = 2 per month<BR>\n" );
document.write( "formula is f = p * g ^ n<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the presen value<BR>\n" );
document.write( "g is the growth factor per time period<BR>\n" );
document.write( "n is the number of time periods<BR>\n" );
document.write( "in t his problem:<BR>\n" );
document.write( "f = 325<BR>\n" );
document.write( "p = 5<BR>\n" );
document.write( "n = number of months.<BR>\n" );
document.write( "g = growth factor = 2 per month.<BR>\n" );
document.write( "formula becomes 325 = 5 * 2 ^ n<BR>\n" );
document.write( "divide both sides of this equation by 5 to get:<BR>\n" );
document.write( "325 / 5 = 2 ^ n<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(325/5) = log(2^n)<BR>\n" );
document.write( "by log rules, this becomes:<BR>\n" );
document.write( "log(325/5) = n * log(2)<BR>\n" );
document.write( "divide both sides of the equation by log(2) and solve for n to get:<BR>\n" );
document.write( "n = log(325/5) / log(2) = 6.022367813.<BR>\n" );
document.write( "confirm by replacing n in the original equation by that to get:<BR>\n" );
document.write( "f = 5 * 2 ^ 6.022367813 = 325, confirming the value of n is good.<BR>\n" );
document.write( "your solution is that it would take 6.022367813 months for the 5 fuzzy quadrupeds to grow to 325.<BR>\n" );
document.write( "that would be in the 7th month.<BR>\n" );
document.write( "here's what it looks like on a graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/041401.jpg\"><BR>\n" );
document.write( "the unshaded area of the graph is between the end of month 6 and the end of month 7. </SPAN>\n" );
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