document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102124>Question 1102124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of inmates N&#8203; (measured in&#8203; thousands) in federal and state prisons can be approximated by the equation N = -2.05x squared + 77.85x + 746, where x is the number of years since 1990. In what year was the number of inmates expected to be 1,280,600&#8203;?  THANK YOU!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716755 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "N is the number of inmates in thousands. If we wrote N = 2, then that means we have 2000 inmates. Going from 2 to 2000 has us multiply by 1000.\r<BR>\n" );
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document.write( "Going in reverse, having 1,280,600 inmates means that N = 1280.6 (divide 1,280,600 by 1000; or move the decimal point 3 spots to the left)\r<BR>\n" );
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document.write( "So we need to plug in N = 1280.6 and then solve for x\r<BR>\n" );
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document.write( "N = -2.05x^2+77.85x+746\r<BR>\n" );
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document.write( "1280.6 = -2.05x^2+77.85x+746 <font color=blue>replace N with 1280.6</font>\r<BR>\n" );
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document.write( "1280.6-1280.6 = -2.05x^2+77.85x+746-1280.6 <font color=blue>Subtract 1280.6 from both sides</font>\r<BR>\n" );
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document.write( "0 = -2.05x^2+77.85x-534.6\r<BR>\n" );
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document.write( "-2.05x^2+77.85x-534.6 = 0\r<BR>\n" );
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document.write( "The equation -2.05x^2+77.85x-534.6 = 0 is in the form ax^2+bx+c = 0, where,<BR>\n" );
document.write( "a = -2.05<BR>\n" );
document.write( "b = 77.85<BR>\n" );
document.write( "c = -534.6\r<BR>\n" );
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document.write( "Use the quadratic formula to solve. Plug those a,b,c values into the formulas below and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-77.85%2Bsqrt%28%2877.85%29%5E2-4%28-2.05%29%28-534.6%29%29%29%2F%282%28-2.05%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-77.85%2Bsqrt%28%2877.85%29%5E2-4%28-2.05%29%28-534.6%29%29%29%2F%282%28-2.05%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-77.85-sqrt%28%2877.85%29%5E2-4%28-2.05%29%28-534.6%29%29%29%2F%282%28-2.05%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-77.85-sqrt%28%2877.85%29%5E2-4%28-2.05%29%28-534.6%29%29%29%2F%282%28-2.05%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-77.85%2Bsqrt%281676.9025%29%29%2F%28-4.1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-77.85%2Bsqrt%281676.9025%29%29%2F%28-4.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-77.85-sqrt%281676.9025%29%29%2F%28-4.1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-77.85-sqrt%281676.9025%29%29%2F%28-4.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-77.85%2B40.95%29%2F%28-4.1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-77.85%2B40.95%29%2F%28-4.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-77.85-40.95%29%2F%28-4.1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-77.85-40.95%29%2F%28-4.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-36.9%29%2F%28-4.1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-36.9%29%2F%28-4.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-118.8%29%2F%28-4.1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-118.8%29%2F%28-4.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9 ALIGN=MIDDLE  ALT=\"x+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+28.9756097560976 ALIGN=MIDDLE  ALT=\"x+=+28.9756097560976\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The two solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9 ALIGN=MIDDLE  ALT=\"x+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+28.9756097560976 ALIGN=MIDDLE  ALT=\"x+=+28.9756097560976\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you want x to be a whole number, then ignore the second solution. In this case, it will take exactly 9 years from 1990 for the inmate population to be at 1,280,600. So this happens in the year 1990+9 = 1999<BR>\n" );
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