document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947586>Question 947586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6% per year. If this trend continues, in which year will 76% of babies be born out of wedlock? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578235 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=578235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with 28%.\r<BR>\n" );
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document.write( "each year that percentage increases by .6%.\r<BR>\n" );
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document.write( "you will multiply 28% by 1.006 every year until it reaches 76%.\r<BR>\n" );
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document.write( "the formula for that is fv = pv * (1+i)^n\r<BR>\n" );
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document.write( "fv is the future value which will be 76%.<BR>\n" );
document.write( "pv is the present value which is 28%.<BR>\n" );
document.write( "i is the interest rate per time period which is equal to .6% / 100 = .006<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "since we are dealing with an increase per year, the time period is measured in years.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "76 = 28 * 1.006^n\r<BR>\n" );
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document.write( "we don't know what n is so we have to solve for it.\r<BR>\n" );
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document.write( "divide both sides of this equation by 28 to get:\r<BR>\n" );
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document.write( "76/28 = 1.006^n\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "log(76/28) = log(1.006^n)\r<BR>\n" );
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document.write( "since log(1.006^n) is equivalent to n * log(1.006), the equation becomes:\r<BR>\n" );
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document.write( "log(76/28) = n * log(1.006)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(1.006) to get:\r<BR>\n" );
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document.write( "log(76/28) / log(1.006) = n\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = 166.9202383\r<BR>\n" );
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document.write( "it would take 166.9202383 years for the percent of babies to be born out of wedlock to reach 76 percent if the rate of increase in the percent was 0.6% per year.\r<BR>\n" );
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document.write( "since you started in 1990, then 166.9202383 years after that would be in the year 1990 + 166 = some time in the year 2156.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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