document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=805876>Question 805876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of Americans (in thousands) who are expected to be over 100 years old in year x is approximated by:<BR>\n" );
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document.write( "	F(x) = .27x2 + 3.52x + 51.78\r<BR>\n" );
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document.write( "where x= 0 corresponds to 2000 and the formula is valid through 2045.<BR>\n" );
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document.write( "a)	Find a formula giving the rate of change in the number of Americans over 100 years old.\r<BR>\n" );
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document.write( "b)	What is the rate of change in the number of Americans expected to be over 100 years old in the year 2015?<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 #485614 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=485614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The numbers that come from that equation seem a bit too high, but I like them.<BR>\n" );
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document.write( "I assume this is a problem from calculus class, that you are expected to calculate the derivative of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29 ALIGN=MIDDLE  ALT=\"F%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and that you know how to calculate derivatives of polynomials.<BR>\n" );
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document.write( "With those assumptions in mind,<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dF%2Fdx=0.27%282x%29%2B3.25=0.54x%2B3.25 ALIGN=MIDDLE  ALT=\"dF%2Fdx=0.27%282x%29%2B3.25=0.54x%2B3.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "b) For the year 2015, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15 ALIGN=MIDDLE  ALT=\"x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dF%2Fdx=0.54%2A15%2B3.25=11.35 ALIGN=MIDDLE  ALT=\"dF%2Fdx=0.54%2A15%2B3.25=11.35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "meaning that the number of centenarians would be increasing by 11,890 a year.<BR>\n" );
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