document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61024>Question 61024</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP! Stabilization ratio. The stabilization ratio (births / deaths) for south and central America can be model by the formula y = -0.0012x^2 + 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 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 is the maximum stabilization ratio from part (b)?<BR>\n" );
document.write( "d. What is the significance of a stabilization ratio of 1?<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 #41955 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=41955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Stabilization ratio. The stabilization ratio (births / deaths) for south and central America can be model by the formula y = -0.0012x^2 + 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( "a. Use the graph to estimate the year in which the stabilization was at its maximum.<BR>\n" );
document.write( "Plot a graph of the given equation: y = -0.0012x^2 + 0.074x + 2.69 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+80%2C+-1%2C+5%2C+-0.0012x%5E2+%2B+0.074x+%2B+2.69+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+80%2C+-1%2C+5%2C+-0.0012x%5E2+%2B+0.074x+%2B+2.69+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It looks like max is about x = 30 years, which is: 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" );
document.write( "Use the vertex formula: x = -b/(2a), a=-.0012, b=.074<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.074%29%2F%282%2A-.0012%29 ALIGN=MIDDLE  ALT=\"%28-.074%29%2F%282%2A-.0012%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.074%29%2F%28-.0024%29 ALIGN=MIDDLE  ALT=\"%28-.074%29%2F%28-.0024%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 30.83 yrs (1980.83)<BR>\n" );
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document.write( "c. What is the maximum stabilization ratio from part (b)?<BR>\n" );
document.write( "Substitute 30.83 for x in the original equation and find y:<BR>\n" );
document.write( "You should get about 3.8<BR>\n" );
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document.write( "d. What is the significance of a stabilization ratio of 1?<BR>\n" );
document.write( "That would mean the same number that die, are born, 0 population growth?\r<BR>\n" );
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