document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118258>Question 118258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The stabilization ratio (births/deaths) for south and central america can be modeled by the formula: y= -0.0012x2 + 0.074x + 2.69 where y is the number of births divided by the number of deaths in the year 1950 + x.<BR>\n" );
document.write( "a)Use the graph to estimate the year in which the stabilization ratio was at its maximum.<BR>\n" );
document.write( "b)Use the formula to find the year in which the stabilization ratio was at its maximum.<BR>\n" );
document.write( "c)what was the maximum stabilization ratio from bart (b)?<BR>\n" );
document.write( "d)what is the significance of a stabilization ratio of 1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86369 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The stabilization ratio (births/deaths) for south and central america can be modeled by the formula: y= -0.0012x2 + 0.074x + 2.69 where y is the number of births divided by the number of deaths in the year 1950 + x.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+100%2C+-2%2C+5%2C+-.0012x%5E2%2B.074x%2B2.69%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+100%2C+-2%2C+5%2C+-.0012x%5E2%2B.074x%2B2.69%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "a)Use the graph to estimate the year in which the stabilization ratio was at its maximum.<BR>\n" );
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document.write( "Maximum looks to be around 30: 1950 + 30 = 1980<BR>\n" );
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document.write( "b)Use the formula to find the year in which the stabilization ratio was at its maximum.<BR>\n" );
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document.write( "Find the axis of symmetry: x = -b/(2a); a=-.0012; b=+.074<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.074%2F%282%2A-.0012%29 ALIGN=MIDDLE  ALT=\"-.074%2F%282%2A-.0012%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 30.8333 ~ 31<BR>\n" );
document.write( "1950 + 31 = 1981 year of max stabilization ratio<BR>\n" );
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document.write( "c)what was the maximum stabilization ratio from part (b)?<BR>\n" );
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document.write( "Substitute 30.83 for x, in the original equation; You should get y ~ 3.83<BR>\n" );
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document.write( "d)what is the significance of a stabilization ratio of 1?<BR>\n" );
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document.write( "I would imagine that means that deaths and births are equal<BR>\n" );
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document.write( "Did this help? </SPAN>\n" );
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