document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=688126>Question 688126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a small suburban town grows exponentially and was 12 000 in 1993 and 21 000 in 1998. In what year will the population reach 36 750? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425547 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=425547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The population of a small suburban town grows exponentially and was 12 000 in 1993 and 21 000 in 1998. In what year will the population reach 36 750?<BR>\n" );
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document.write( "Form : A(t) = ab^t where t is # of years after 1993.<BR>\n" );
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document.write( "Solve for \"a\" and \"b\" using (0,12000) and (5,21000).<BR>\n" );
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document.write( "Using 0,12000 you get: 12000 = ab^0<BR>\n" );
document.write( "So a = 12000<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "A(t) = 12000*b^t<BR>\n" );
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document.write( "Using (5,21000), solve for \"b\":<BR>\n" );
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document.write( "21000 = 12000*b^5<BR>\n" );
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document.write( "b^5 = 21/12 = 7/4<BR>\n" );
document.write( "b = (7/4)^(1/5)<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "A(t) = 12000*(7/4)^(t/5)<BR>\n" );
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document.write( "In what year will the population reach 36 750?<BR>\n" );
document.write( "Solve:<BR>\n" );
document.write( "36750 = 12000(7/4)^(t/5)<BR>\n" );
document.write( "(7/4)^(t/5) = 3.0625<BR>\n" );
document.write( "Take the log to solve for \"t\":<BR>\n" );
document.write( "(t/5)log(7/4) = log(3.0625)<BR>\n" );
document.write( "(t/5) = log(3.0625)/log(7/4)<BR>\n" );
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document.write( "t = 1.68 years<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "================== </SPAN>\n" );
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